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Jorge Pullin: Okay. So our speaker today is Luca Market. We will speak about developments in group field theory, cosmology.
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Luca Marchetti: Yeah, thank you. So first of all. I wanted to thank the organizers for inviting me, because this and I want to be able to speak today. And before talking about the development I wanted to emphasize that
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Luca Marchetti: all the results that I'm gonna talk about doing the talk are actually due to the amazing work of many different people that I try to list here. So yeah, and if I forgot somebody this forgive me by. I wanted to emphasize the collective nature of the effort.
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Luca Marchetti: So the plan of the talk would be the following: First, we will introduce theories, and we'll review the main ingredients that are gonna be useful for understanding the general strategy that we don't follow
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Luca Marchetti: in order to look so cosmological physics from this kind of models.
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Luca Marchetti: And that's going to be the second part of the talk. When we're we're gonna outline this general strategy and show Sha applied first, you know, to start the Museum, and as a topic sector of small.
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Luca Marchetti: So we review some old results. So, but in a new perspective, and I will report on some new results.
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Luca Marchetti: And I will also report on other new results concerning the
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Luca Marchetti: Okay, so i'll start by introducing a few theories.
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Luca Marchetti: So here is our period of a field, the final decoder with manifold. So we're going to consider geometric models. So G. 4 S. Is going to be the dimension of the space, and to be so d is going to be fixed to 4.
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Luca Marchetti: Ng. Is going to be the location of gravity. So G. Is going to be a. To see, or in some of the cases that are actually going to be the most interesting one for the rest of the talks
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Luca Marchetti: we can actually stick to subgroup on the set to see, and if I can ask you to. and I will come on this point to later.
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Luca Marchetti: So most interesting peculiarity of these theories is that the interaction terms are. and when this will mean that the arguments of the field that appear in the interaction terms
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Luca Marchetti: following the from the other part, that it by a certain graph that is included in the
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Luca Marchetti: So if you wanna have a picture of this kind of interaction, it is 5 dimensional by order, 5 in
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Luca Marchetti: out, to glue, or to to to to convert this. It's this viable and specifically the details of this convolution.
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Luca Marchetti: And this is particularly important, because it turns out that rising the the final tigers on the theory.
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Luca Marchetti: they turn out to be stranded diagrams which are in fact, dual to the dimensional cellular complex, is a.
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Luca Marchetti: So when one brides the amplitude associated to these diagrams they become sums over group theoretic data associated to a cellular conference.
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Luca Marchetti: and that means that if we choose the magnetic, we could match a as painful offices.
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Luca Marchetti: and in particular, this also means that the partition functional, digital.
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Luca Marchetti: written. But if there is a some over 500 diagrams, we provide us with a complete definition of being forward. So this is a one way of seeing this group field theories as really providing, providing us with a a complete definition of being from home.
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Luca Marchetti: There's also another point that I wanted to, and for sign on the aspect of this that is important, and this is the connection with the
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Luca Marchetti: and this is it is especially in my first if you look at the one particle in my space
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Luca Marchetti: of this year, so the one particle in the space, in the after, the in position of appropriate constraints.
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Luca Marchetti: and these constraints are encoded in the genetic and interaction kernels of the action. and and they allow us to have a a demonstration Interpretation of this.
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Luca Marchetti: together with the these constraints usually are divided into closure and simplicity constraints. So if you associate this
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Luca Marchetti: to the faces of the instead. The simplicity, constraint is more model dependent.
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Luca Marchetti: and, for instance, for the backing model, it just tells us that the faces of the I have to I on the same surface, so which is on the same upper surface, which is specified with respect to normal X. Here.
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Luca Marchetti: you know, while in the model, because, you know, sign like a singer for but now it includes.
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Luca Marchetti: and for the rest of the talk i'm going to focus mostly on this on the April model, and I would just mention from time to time the differences in the I this that would appear in the by.
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Luca Marchetti: and having this simplician interpretation for the month from the one that I want to, and closing program to be able to train, allow us to make some some connection with quantum gravity. And this particular is it in the presentation space
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Luca Marchetti: in the case, if you impose simplicity, which can we reduce to as you 2 data after imposing also, you can say what we find is that it's a space of the one parting or the space of the material
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Luca Marchetti: is nothing but the but an upsp network vertex space.
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Luca Marchetti: So from this we see that the fundamental point of fundamental structures that we find in the are similar to what we could see as we know at this option.
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Luca Marchetti: However, when we look at the hidden spaces of the theory, there are some differences that I would like to. So in the 50 we can certainly construct the
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Luca Marchetti: fox base, and we could also buy in a kind of methods. So, for instance, by introducing the and it's actually acting on the on the on. The
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Luca Marchetti: But 1 point that I want to remark is that the space of states which is associated to connect a simply a complex season.
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Luca Marchetti: He's only strictly contained in this goofy theory, Fox space.
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Luca Marchetti: and this means that United States do not respond to connect the a lot this is, nor to classical.
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Luca Marchetti: So, in a sense, the good feature, fox, base is female to the, but also different in the sense that No, in continuing to at all in particular, there's no in position on all.
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Luca Marchetti: And also to an it is, is is defined with respect to notes rather than to grab. So this is a consequence of the fact that the in group of theory we have this member drops into fundamental nodes and notes have such a prominent feature.
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Luca Marchetti: whoever it is still quite important to from the perspective in like a connection we look on in reality, because this allows us, for instance, to import it some very useful physical insights in the theories in particular, it allows us to construct a simple one. Size operators
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Luca Marchetti: with with with some clear. For instance, your magical meaning, and the way this can be done is by the usual same quantization prescription. So we takes a we send which magic. It's been natural states between appropriate powers of the 500.
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Luca Marchetti: There's an example of this kind of operators. We have the voting operator which is gonna be very important for the rest of the toll to, and which is essentially and contribution, we
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Luca Marchetti: the last ingredient that we need, you know, from the general perspective about we 15 is the introduction, the introduction of multi fields. In particular. We will be focusing on scout fields except for for for for for for a few cases.
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Luca Marchetti: so we need to understand how to couple. and the strategy is the same. It will be for a dramatic Bible. So we look at the spoonful arguments.
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Luca Marchetti: So at that level we can discretize this kind of feel over at the Simplex.
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Luca Marchetti: And this also means that each demise from Simplex that composes the Simplex now for carries the value of the discretized per field. and using instead one category. But they have to be the the company with the space has to be a lot more than to
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Luca Marchetti: also a comfort is condition on the is of freedom, and it's a consequence. So the the the domain needs to be enlarged in, you know, to generate this kind of form.
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Luca Marchetti: One difference, however, between a and a new local, and can be a sort of fashion interactions, for the reason that I mentioned before
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Luca Marchetti: Why, it's kind of because the way we have the we have, and it is exactly because these kind of interactions are mimicking the reconstruction of the the growing of the demons. One sympathies to form a d simple
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Luca Marchetti: And so we are interactions. There are first simplifications over there arise, for I mean my couple of the free and my Cisco field, though, which is gonna be in our may not be in this talk.
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Luca Marchetti: because in this case the
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Luca Marchetti: and
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Luca Marchetti: so
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Luca Marchetti: these are really the the the main ingredients that we need in order to all discuss about the the the strategy and to extract the technology. So let me now review this strategy.
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Luca Marchetti: So the first step is to look at the
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Luca Marchetti: And so, as I said before, from the the perspective. Continuing geometries are associated to a large number of.
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Luca Marchetti: because we don't have in general a notion of continuing in the in the full full space. But we do expect this. This continuing geometries are some more associated to having a large number of.
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Luca Marchetti: and the simple states that can actually accommodate this infinite number of are, in fact, the common system. It's a Here you see the simplest and of the one body common state which depends on you data, and
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Luca Marchetti: at 1 point it's awarded. The marking is that when the group interactions as well, which is certainly so, this 5 in a broken region, because they're defined as the theory starting from a, and it's it's perturbative expansion of the partition function interior.
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Luca Marchetti: then the dynamics of the
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Luca Marchetti: is actually the I mean by these averages. and it is nothing but a midfield approximation of the full provision function.
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Luca Marchetti: So, in a sense, even though these States are remarkably simple, they already allow us to have the access to some in particular. But the information
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Luca Marchetti: the other ingredient that is worth mentioning is that, of course, is our background in the balance quantum for theories.
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Luca Marchetti: So we we need to in order to struct some notion of locality and of evolution. We need to do so in a relation one, so we need to construct relation on the
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Luca Marchetti: doing so. In general. In the graffiti fox space is particularly difficult. First of all, because these are part of the series; and second of all, because there's no continue intuition. As I said before, that I've been on the full.
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Luca Marchetti: Whoever one can construct a an effective notion operational organization at the level of observable averages.
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Luca Marchetti: and this, for instance, can be achieved, as we will see in a moment by considering these comments with something here
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Luca Marchetti: played into a fixed picking function. I will pick on the on the Creation from the account fees that we want to use to to the reference frame. and I'm. I'm. I'm. In the with this.
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Luca Marchetti: So let me show you now how the works. So in the simplest case of the
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Luca Marchetti: So we first of all, we introduce a a notion of all united with respect to our relational frame, so we assume that the concept we function only depends on me on a couple of masters and free clock scarf field.
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Luca Marchetti: So it's domain. Turn out to be equal to me. So for space, plus, of course.
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Luca Marchetti: and when you need to look at observable, of course. and of course I've already introduced the the most relevant to magic observers for the on the genus and the topic sector, which is the volume operator.
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Luca Marchetti: but having into having to use all the plots, kind of feel he does access to scout field, several, sometimes operators. For instance, here we are. We we have the from one.
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Luca Marchetti: Moreover, it doesn't it's kind of important viable in the fox space that would play a crucial role, as we would see in a moment, which is the number of data.
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Luca Marchetti: Now, when we take it, we can values of these operators on our picket states. So so on our Korean picket states on our we are on our clock, viable on our on an arbitrary point of picking that we call. That's not.
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Luca Marchetti: You may come, of course, just 5 months of the reduced come to it from. We can localize the to point itself.
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Luca Marchetti: And Why is it not important? It is because an X not is just the equivalent of the
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Luca Marchetti: our feed operator. So it's the expectation value of our clock. Viable.
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Luca Marchetti: Oh, this allows us to construct effective relation. Observ. It was provided with. Some conditions are satisfied. First of all, we need a zoom call for the situation, because we want the question to capture the right. Now, physics for the clock.
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Luca Marchetti: Second of all we want, that the we can with respect to this example is essentially generated by the expectational body of the moment.
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Luca Marchetti: and, as it turns out, both these these conditions are satisfied in an appropriate regime that we would see later, being a related to the cost of.
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Luca Marchetti: So let's not look now a little bit more on how these expectation bodies actually look like.
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Luca Marchetti: We will do so by imposing a an important approximation that is going to be the the the, the the condition of wave function, as so of all the geometric information that the wave function contains. So
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Luca Marchetti: in general it contains. It depends on on for spin. So in the twin labors
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Luca Marchetti: we assume I don't want to be. Which means that all this zoom magic information is not collapsed to a single spin viable
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Luca Marchetti: also. Here I've used the unified notation, because it turns out that this, this, these results that have been direct first for the Api, like model, can be reproduced exactly in the same manner, also for bottom frame mode.
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Luca Marchetti: So here it is. You can try to be in the case of the URL, or a real font in the case of the
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Luca Marchetti: as you see, because the now the expectation volume of the volume, and the number of
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Luca Marchetti: on our on our States of winters. Now it's because somewhere in integral of these, in this case the I can part of the volume way to buy an economy with function, and in this case, just by the
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Luca Marchetti: from this is that the the mechanism that makes the volume grow.
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Luca Marchetti: It's the fact, the number of, and they are going. So if the number of ones are growing, the voting itself growth, and this already tells us that a large volumes, which will we will, the Navy associate to classic
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Luca Marchetti: large number one, which was our initial guess. and, as we will see later, this is a more precise, this, this. This can be made into a precise statement about the classical limit
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Luca Marchetti: of these models.
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Luca Marchetti: The other important point to make is that both the volume and the number of greater dynamic is eventually determined only by this reduced kind of with function.
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Luca Marchetti: So how is the
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Luca Marchetti: so? As we said, we want to compute this dynamics in the new field approximation.
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Luca Marchetti: and one so in in in this main field approximation. We will also neglect interactions. And this is an important assumption
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Luca Marchetti: which is a compatible, of course, with our requirement of Evan's move interactions from the beginning. but it's not gonna be valid throughout the whole evolution of the universe.
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Luca Marchetti: because eventually interactions will become dominant. And so this approximation would back down.
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So it is important to emphasize that this approximation can only be valid for a.
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Luca Marchetti: On top of that we have another interesting property of our picking picking States, because they allow us to perform a a derivative expansion of the kinetic kernel. With respect to our clock viable, on which we are picking.
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Luca Marchetti: and this, together with the conditional iotropy really makes the equation. For the
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Luca Marchetti: all information about the details of the model is now encoded on this key parameter, and on this that the information. The State is also in that on this final part.
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Luca Marchetti: So there I am, for the volume given. These equations of motion is the one that You see here and there are 2 important limits that I want to remark. The first is the classical link. So this is associated to having large
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Luca Marchetti: density, so large models of the
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Luca Marchetti: to having the large number of and dynamically it turns out to be related to late times.
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Luca Marchetti: So in this limit, if we find, if we have that this new parameter which is related to this here is only my depend on our presentation label, and equal to 3 by
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Luca Marchetti: then, and and the way that we find for a while you become the cloud. Also we can look at the quantum fluctuations on our on our variables. Both the gl and dramatic variables.
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Luca Marchetti: and it turns out this one. The fluctuations are under control. It is exactly because these fluctuations are controlled by the average number of points in the condensate. And here we are in the link meeting, which is number one, that is, is quite large.
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Luca Marchetti: So this really characterizes this, this renewable theory as the classical
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Luca Marchetti: when we start, go at the earlier times. What happens is that there's a non-zero. Volume balance for a a large range of initial condition we call it. We have a included into these. From there's 2 and a half beyond that. Define the initial conditions for our.
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Luca Marchetti: but it's an important point to make here, because, as we go at barely an earlier times, what happens is that, of course, the voting we're smaller, but at the same time the number of quanta.
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Luca Marchetti: So it is possible that the bounce happens in our genome, where the number of quanta is quite small, and this regime we might have large on fluctuation, both in the volume and on the clock by us.
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Luca Marchetti: So if we have large quantum fluctuations on the volume, this means that this is this equation here which is right for the expectation volume of the volume. It's not reliable anymore. It doesn't capture any more. On physics.
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Luca Marchetti: On the other hand, if quantum fluctuations on the clock are large, then it means the our effective approach to describe your rationality.
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Luca Marchetti: A. It's breaking down, so we cannot again, we cannot rely on the separate, for
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Luca Marchetti: so the we can rely on the bouncers out as coming from this equation. Here is the initial conditions. Our States are such that the the bounce happens when the number of one down by stick, but large.
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Luca Marchetti: So let me now move a little bit towards a different kind of matter, because so far we only consider the a and a couple of masses. And
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Luca Marchetti: so now let me consider a massive, a scalar field that with the no 0 potential. This is especially interesting for the greetings, first of all, for phenomenological reasons, because this kind of scarf fields are all internal stuff for inflation and physics.
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Luca Marchetti: but also this is especially interesting because it forces us to look at the video interactions, because this is where the the scoffing potential would act there.
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Luca Marchetti: So we did study these interactions conservatively at late times
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Luca Marchetti: in If you are luck, if you are like model, and in a single spin approximation, and we have considered different order in different structures for the interactions.
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Luca Marchetti: We've considered the fiscal monitoring interactions where you see, there's a a balance between the 5 bar and 5. So the complex one you get to feel that in the interaction term.
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Luca Marchetti: and we did find that there is a possible G. Are matching, but only if L is equal to 5. So if the ordinary interaction is actually 6,
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Luca Marchetti: and if the microscopic constants, including the gravitational coupling, run, we relation of time, which is a result that I would like to comment on at the end of the talk.
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Luca Marchetti: So we've been also looking into phase interactions which are directions which there's
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Luca Marchetti: completing balance between a 5 and 5 bar
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Luca Marchetti: fields. And in this case we again can find a Geo matching for a 4 and 6 interactions, and by applying the the
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Luca Marchetti: the the microscopy constants to run.
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Luca Marchetti: But we also find that this the fact is call free and potential. So the potential that emerges from from the gets actually corrected by to go magic factors, and these are results that it was also on late time. So it seems to be a result that should be true also
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Luca Marchetti: in a regime which we will call the classical regime. Looking at what we have seen writing design before.
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Luca Marchetti: and this suggests that there might be interesting chronological consequences for these results that we haven't explored yet
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Luca Marchetti: another comment I would like to make. Here. We've seen matter being introduced, being coupled in the 15 models by starting from the
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Luca Marchetti: But, as it turns out, there is also a way in which exoting master can a marriage you just as a result of your
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Luca Marchetti: Indeed, if I consider this modest interact, or there's 6 months in very late times. But now you also include the
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Luca Marchetti: What you find is that the W. Enters in the equation of of, of, of, of of the dominating fluid in the universe. So this far is this equation here.
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Luca Marchetti: but the universe in product is going to be effectively dominated by an emergent font on dark energy, which is not pathologic, because if you were to introduce these emergent fonts and that energy by hand of the
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Luca Marchetti: then you would encounter documents, stabilities, and all sorts of problems.
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Luca Marchetti: But in this case this is just an effective behavior that is arising from the from purely contemporary effects as dictated by the interactions.
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Luca Marchetti: So just here I just wanted to emphasize that there are 2 different ways in which matter kind of dealing with 15 models. One is by is by adding it by hand.
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Luca Marchetti: and the other one is by looking at the impact that, for instance, school 15 interactions may have in the late time emerging the effective dynamics of the volume.
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Luca Marchetti: So now are Are there any questions?
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simone: Yeah, we go to the Virginia sector. Can you remind us what the
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simone: tells you that they.
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simone: your large volume is made out of atoms which are well separated, and not just crumbled up one on top of each other.
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Luca Marchetti: What they mean exactly by trumbled up like, because not, since there's no graph structure at this level. It is even difficult to specify in which sense we can talk about the problem because you have mapped there. For instance, you can look at the correlation of your
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simone: matter field across different atoms and see that they decay with some notion of distance.
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simone: because if that doesn't happen.
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Luca Marchetti: even though you see an equation that looks like Friedman. I don't understand why you can interpret it as some semi classical behavior. So we we can look at matter. What we do here is a look, also the dynamics of matter, even in both in the case with the potential and without potential.
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Luca Marchetti: And we look at the, at, the at the equations of motion for matter.
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Luca Marchetti: and they turn out to be exactly the classical equations of motion that
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simone: you could say you don't even need a potential, you would say, just a ticket. Your field file. Your matter is 5
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simone: on one atom and on another atom, and you compute the expectation value of this correlator.
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Luca Marchetti: Yeah, I I see what you mean. But in this case we have. We have just a a collective state. So we're not considering States with just one out of our or
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Luca Marchetti: we we 2 autumn separately. So we, if we take an expectation value that is going to be over the All condensate.
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simone: Okay, Thank you. So so you you you can see explicitly the difference between one out or another one, because in the condensate state you are, you will have a superposition of influencing many atoms.
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Luca Marchetti: I don't know if it's this.
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Ivan Agullo: Go ahead.
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Daniele Oriti: Yeah. Yeah. Did the just to rephrase what to look at. Just answer, which is which is the answer I mean. The point is that at this level of description you have entirely, if you want Course grained the the description in terms of tetrahedra and triangulations
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Daniele Oriti: in a very simple state. But you only look at the full collective behavior.
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Daniele Oriti: Even if you had considered the genetic superposition of genetic triangulations at this level of description, you will not see the triangulations anymore. You will see just the result of the full sum.
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Daniele Oriti: So if you want, if I want to ask, answer your question in in terms of physical quantities, I would have to define the correlator of the scale of the at this effective level which it requires. It is in homogeneous degrees of freedom. I need to define the location of 2 scalar fields
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Daniele Oriti: and compute the the Dk rate of the resulting correlation. But in this effective and level, not in terms of triangulation or graphs. So because I wouldn't see them anyway.
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simone: No, but forget the graph. So doesn't this kind of feel couple to your atoms. So even if you have infinity, many atoms, you could evaluate the interaction between the scalar field and the atoms right.
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simone: and maybe just use that.
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Daniele Oriti: Anyway, I don't know.
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Daniele Oriti: So I mean there is a scalar field value for each atom.
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Daniele Oriti: In the type of state we have that there's no correlation between atoms. So for the very nature of the mean field approximation. The atoms? No. But you who compute the correlation of the scalar field of one atom with the condition of this care field at the atom or the other atom couldn't you?
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Luca Marchetti: Yeah, I mean, if you, if you, If you wanted to do that, you you could probably define the correlation on discount field with respect to dramatic Bible, so you would have to write the relation observable for the scarf field with respect to geometry, and then, in principle, you could compute the like a core like a 2 point function, for that.
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Daniele Oriti: Is that what you're suggesting? But not in the state.
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Daniele Oriti: No, i'm not in this state. No, no, no, exactly not in this State State is uncorrelated from the point of view of the math, the degrees of freedom on the Tetrahedra, because it's a. You know it's a superposition of product states.
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Daniele Oriti: But you can ask the question in physical terms, You know, in the effective description. If I compute the amp you for the scalar field at one location and down to the scale of the different location. So in this homogeneous sector you can ask how it scales.
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Daniele Oriti: how the correlation scales! But at that level
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Western: there is a question also. By Western, I don't my thank you. I, before going ahead in order to understand what is coming up. I would like to to understand better. How do I interpret the geometry of this design, and say it's where it's so it's a. Related to some, also to the question based on it, Where do I read which javascript? I am describe you whether this is a sphere or it's somebody else. It's that's basically a week
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Western: like this, or what?
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Luca Marchetti: Well, for instance, you can see it already
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Luca Marchetti: the level of the dynamics of the volume, because it really satisfies the flat pretty much to work in the house.
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Western: So you, you don't have spatial conversion in this sense.
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Luca Marchetti: Well, the States are extremely simple in this sense, as Daniel said before, because we have no correlation between the fundamental one. Or so.
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Luca Marchetti: strictly speaking, there is no graph structure at the level of the States.
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Luca Marchetti: Still you can recover different properties for the dynamics of the of the of the geometry.
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Luca Marchetti: and that is determined only by the effective field of equations.
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Western: No, this is connected with what is coming next to, because in the moment in which you want it to describe the day, you know in it some of the perturbation you need to tell me which you you're working, and you will have your You will expect a different results depending on the
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Luca Marchetti: Yeah, I in a sense, yeah, you're absolutely right. I I didn't. I didn't want to spotted the results. But in the end we would see that in order to write to find some dynamics for the preservation that is actually compatible with the gr one.
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Luca Marchetti: We need to include some form of correlation in this kind of clearing states, and these are going to be dipole correlations. I didn't want to spot it already. But you guess it right. That's that's what gonna what's gonna end up? Yeah.
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Western: Okay. I I wait for the night. What is coming next? Thank you. Okay.
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Ivan Agullo: Daniel, you do. You still have? Do you still have to comment on this.
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Daniele Oriti: Yeah, just a brief comment. I think that the
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Daniele Oriti: it's misleading To think that you have to specify what sort of geometric properties you have when you write down your state that then you do some coast-graining you do some, you know, procedure and you instruct an effective continuum dynamics.
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Daniele Oriti: because if you knew what dynamics, and what sort of geometry you would get. It's unclear, what? You're trying to look for
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Daniele Oriti: the the Our perspective here is exactly that clearly the resulting geometric properties
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Daniele Oriti: and the resulting, you know, evolution of geometry will depend on the States.
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Daniele Oriti: So we are trying to find out what the geometric properties, and what dynamics we can instruct for different type of states starting from the simplest mean field approximation.
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Daniele Oriti: So if I ask what sort of geometry corresponds to the state we use so far in the homogeneous sector. The answer is what Luca gave. So there is an equation for the volume. This is the effective proper the effective dynamics of the volume for such a state.
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Daniele Oriti: Really, the moment you start computing other observables.
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Daniele Oriti: you will find more information about the resulting geometry of these States. They may find out that that you know that 2 trivial is too simple an approximation to reproduce the the correct behavior of a number of other observables.
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Daniele Oriti: But the the way you ask the question is indeed you take a state. and then you compute the observables.
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Daniele Oriti: Is not the you decide that your state corresponds to a certain geometry.
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Daniele Oriti: and then you, you know you instruct. I don't know exactly what at which point.
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Western: please. That's how we? We we are approaching the issue.
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Western: Are you okay? That's when you complete the transition. I'm: which is in general, and you are, You know what what are your states, and and you commute to the probability.
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Daniele Oriti: Yeah, of course. But what I don't agree with is the fact that what you put there, what you read out of the the triangulation description is in itself any guarantee, or what is going to be the effective continuum behavior.
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Daniele Oriti: because if that was the case. Then somehow you are assuming that the course graining is trivial.
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Daniele Oriti: that nothing happens when you put together all these degrees of freedom, and that's exactly what we we don't feel we can assume, and we are trying to find out what is the effective done on this
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Daniele Oriti: with with various different states.
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Western: I mean, i'm explaining what we're, how we are proceeding.
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Ivan Agullo: Maybe we should continue and look at this question in the chat Free lady, to your last slide. The question is whether there is a inflation.
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Luca Marchetti: Oh, yeah, I I wanted to talk about this in the conclusion that I can already say something about it. So regarding the balance already is not enough to in the an inflation that is sustained for long enough.
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Luca Marchetti: But one question that we were wondering is, if these of to remind you, correct to the potential. The web drive only a late times, for now
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Luca Marchetti: are also present at 30 times, because if that's the case, even having, for instance, the flop potential for the car field it could generate because of the the facts could generate an effectiveness that has something to automatic po properties, and it would look seem like in green simple, not exactly the same form to natural inflation. So we we we wanted to look at that, but we haven't done that yet.
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Ivan Agullo: Thank you. Go ahead.
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Luca Marchetti: Okay. So now let's move a little bit more towards the sector, and before I I go home to details. So I wanted to clarify a a a more point, which is a really, usually, when one talks about extracting the homogeneous sector of cosmology
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Luca Marchetti: from continuity. There are aspects to get some of our meet together. and one is the initial conditions aspect of the program, and the other is the dynamics of the
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Luca Marchetti: so the in principle, if I have some emerging probation dynamics for this, for for this in the
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Luca Marchetti: then you could for quantize that, and that's, and and then we provide us with the way to address the initial conditions problem.
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Luca Marchetti: Well, of course, from the perspective, it is a lot more appealing or or ideal. If you want to to extract these quantum properties directly from the 50, or from from the quantum going to the or you in this case the fifth year.
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Luca Marchetti: A first step in this direction has been taken over by by comparing the the second moment of the relation, one operator to the promoted power spectrum.
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Luca Marchetti: but they still leave some questions open up like, what about tired moments? Can we actually prove that these is? Gosh, and especially because we're talking about? Possibly early times, when when this kind of quantum effects might be in boil, and
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Luca Marchetti: the other natural question to ask is, whether or not this relation one operator is re iteration of this kind of a tricky question to ask, to answer from the full quantum gravity, or if you do perspective
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Luca Marchetti: and the last question, but it's still how this result is impacted by the participation dynamics itself.
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Luca Marchetti: But of course, these that there are open questions, because this is a obviously a very complicated task in general, because it means extracting the the quantum field theory on curve background, the limit of the underlying. So it is particularly complicated.
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Luca Marchetti: A little bit simpler is to in the dynamics of the classical. But still it is. I don't know, trivial, because you need to start the dynamic. So back to the
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Luca Marchetti: I got a first up in the directions being taken for scar perturbations in the separate universe framework.
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Luca Marchetti: But and at this point the initial extension would be to reperform the in those case, possibly using a proper physical reference ring.
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Luca Marchetti: And this is second point. The problem is what i'm gonna talk about about for for the remaining on this store.
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Luca Marchetti: so to extend the analysis to to allocate. So i'm. Using a relational frame, we are considered the simplest to study relation and regional system
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Luca Marchetti: we've classically given by for you my couple of masses and 3 reference fields and one mean like a couple of months and 3 month a field which we as soon to be dominating the to budget, and which was soon to be exactly really sharing, homogeneous with respect to our
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Luca Marchetti: at the bottom, level, if that we have a good 58 field, which now, should the ban on the group viable on our route, and and we we the clock or a frame field viable, and on our monthly.
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Luca Marchetti: and we work within an if you are like model, though with the goofy reaction that we that's the classical.
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Luca Marchetti: and we can please exactly as before. So we can look at observables first.
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Luca Marchetti: and these observable are going to be a frame and multi-believable and of course, also the you magic observers.
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Luca Marchetti: So this point we we're gonna restrict the again only to the bottom operator. But this is going to be an important restriction, because we're only going to work with that. We're only going to extract the license, or we can scholar information about perturbations. Because of this
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Luca Marchetti: regarding States, we will consider again collective states like the one body Korean states that we discussed before.
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Luca Marchetti: which are gonna be picked around our around our frame variables because we still want to retain that notion of relational organization.
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Luca Marchetti: and with the peaking on our route, which is going to be asotropic. And same, we assume that the we function also contains all the atomic information. All these assumptions are compatible with the fact that we can only address the boarding operator at this point.
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Luca Marchetti: And where do we include emotion? Id so we do so at the level of the models of the Commons that we function. So we've got to have a background point with the with the
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Luca Marchetti: and if you perform the the usual meetings
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Luca Marchetti: by assuming their interactions are negligible, and by focusing on a single PIN approximation. We can find equations for both the volume and the in the month. And now
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Luca Marchetti: and what we find, of course, is that this is actually, one important point is that 2 operations actually in the couple a late time since. So for a large number of points in this, in 2,005,
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Luca Marchetti: and one obvious result of this is something we already found in before. When I'm. Talking about this in the potential is that there is matching with you are. But something more interesting happened because of the perturbations, because, although there is a there is super rise on matching with the R,
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Luca Marchetti: it's actually no matching for intermediate and to Verizon modes. So, as first we thought that the problem might have been related to the, to how we coupled our free variables.
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Luca Marchetti: And and this actually led us to some, some interesting approach to the problem. They actually solve this issue. So I will come to this in a moment. First of all, I want to explore a little bit more to physics of this Verizon presentation, because this is especially interesting
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Luca Marchetti: a 30 times, because we have the of the most of the perturbations are, in fact, super horizon. so the only time.
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Luca Marchetti: of course, in this case the questions become much more complicated, but we were able to rewrite these equations in a close manner for the bottom operator. And we're also actually able to compile and compare it with the the dynamics of the animal if I go here in this Verizon name, because, as it turns out to for summarize most, as there are equations that capture the the the dynamics of these modes for.
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Luca Marchetti: and the result was that there is actually no matching at 30 times. So between any one, if I go to theory. And then i'm studying. I just from this with 50 years.
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Luca Marchetti: Not only that, Yes.
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Ivan Agullo: So what question this issue with Sapph horizon modes it happens. Any value of the Hubble right? You know, no matter how low energy. You know how a small have a right at this, you have that issue.
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Luca Marchetti: Yeah, yeah, because the the the the the of the radius is is essentially the but the background, the bridge. So once you put some particular initial conditions for for use. Conf. So you once you decide the energy dance. If you want to, on the discount fields, you'll get an apple, a number of parameter, and then you can look at perturbations, and for anybody you're gonna find the the same exact problem.
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Luca Marchetti: But yeah, I I will discuss in a moment, though, how this program can can actually be addressed.
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Luca Marchetti: and it is actually related to also what to all Francisco. So before
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Ivan Agullo: Thank you.
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Luca Marchetti: Yup. So so that's only we can get the this early time supervised most dynamics tool. Well, if I go with you, but we also compare it to the dynamics that you would obtain by perturbing only the background with 52,
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Luca Marchetti: which is something that.
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Luca Marchetti: So it turns out that this also these 2 dynamics do not match it every time. So this already suggests that when we look at the quantum person presentations, or in more than any, even in the simplest case, which is a supervisor.
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Luca Marchetti: perhaps the behavior. We we should be quite careful, because the behavior that might appear from the full quantum theory might be different from that that arises by using a, for instance, modified gravity theories, or by just relying on the background. That
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Luca Marchetti: So now let me tell you a little bit more about this super supervised on our intermediate case problem. So first, as I said, we were thinking that the problem was was related to the
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Luca Marchetti: to having a to not having coupled properly the frame degrees of freedom. So, in order to to start, it is phenomenal or more in detail.
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Luca Marchetti: we we decided to look into a model we on which we have
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Luca Marchetti: a clear control over the course of properties of the phenomenal quanta, and this is the complete extended marker in moment. So in this case you have different.
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Luca Marchetti: which generate which we different to causal properties which are specified by it's normal and normal. Originally it was introduced to in order to impose the enclosure, and this is the constraint in a Covid one. And so it's just a very viable. It's absolutely UN dynamical.
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Luca Marchetti: but it allows us to, for instance, the construct fox space, which is.
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Luca Marchetti: which is a two-second folkspace.
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Luca Marchetti: So in general creators they will doc on this fox base. We'll correlate in space like and download it to either, except for the ball, and which, of course, is only the final
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Luca Marchetti: Having these different kinds of really helps in understanding how to couple the frame fields, because we do know that we do expect that the clock field should propagate along a time like Google Edges.
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Luca Marchetti: And this kind of propagation is, in fact, encoded in the in the genetic kind of
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Luca Marchetti: on the other one, on the other hand, the rods Bibles. I started to propagate along space like
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Luca Marchetti: dual edges, and therefore and this is encoded in the kinetic kernel for a time like this. So this already helps us trying to address the problem of frame coupling in a more clear manner.
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Luca Marchetti: but also when I we try not to explore a different direction regarding perturbation. So before we have, we had implemented perilations at the level of the one body condensate.
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Luca Marchetti: Here we follow a different approach, and we we we we were considering the background. We we were clear of state, which is here by this day this year.
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Luca Marchetti: and we it's part. So there's the background part which is given by the space like.
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Luca Marchetti: and these are one body from the face. I think the function here are very, you know, home. So these are the background quantities. and we assume, of course it is a big as before, because we want to see everything from now
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Luca Marchetti: rational organization. But what is interesting is that the now we're including perturbation in nearest neighbor to body correlation.
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Luca Marchetti: and these are correlations that, including the
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Luca Marchetti: and if we run again a for for these kind of states, what we find in the end is that the first, or that there are 2 couple of equations for 3 Bibles, if there's applied on the plan of the flight.
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Luca Marchetti: But Most importantly, when we write the evolution for the equation for the volume.
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Luca Marchetti: we find that if we required this evolution of for the volume to match Gr. Late times. This completely fixes the dynamics of this. We have free dynamics for one. It's reliable.
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Luca Marchetti: also 50 parameters that I mean in the end, late. And then you have make all of the I'm. A comment that we can do in the by by itself, so we wouldn't have access to the by looking at the board.
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Luca Marchetti: So in this case we do find that that it is possible to match Gr. That the late time phone presentations magic are at those scales, and the important physical insight is that these perturbations are actually 2 body correlations at the level of the full.
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Luca Marchetti: So let me now summarize the main results and and give some perspectives.
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Luca Marchetti: So i'm gonna divide the discussion between early late times, because maybe it's a little bit useful to to to distinguish between the 2. So at 30 times we find that there is a singularity resolution into quantum bounds.
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Luca Marchetti: and this result seems to be a universal in the sense that it seems to both for the IP URL like model and the extended by cream mode. But keep in mind that we are pulling this just for me my couple of masses and frisco fits as well.
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Luca Marchetti: Also, we have been able to study the impact of quantum effects on the bounds and their interplay with rationality, pointing out the the relevance of the an average number of point in the condensate to
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Luca Marchetti: to regulate the the the impact of these quantum effects.
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Luca Marchetti: What's another point that I I
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Luca Marchetti: just doing the question before, is that actually the acceleration? Because this is not long enough to sustain inflation?
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Luca Marchetti: We find that in the regime where interactions are small, we can identify proper classical regime, which is characterized by small quantum fluctuations and appropriately are matching. And again, these results seems to be classic. This seems to be universal
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Luca Marchetti: for me. My couple of named Moses and Frisco Fields, in the sense that he's recording both in the burial, and in
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Luca Marchetti: we we're also. We also started a a scarf field with potential, and we found a a late times that in order to match the R. We need the the companies to run in time.
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Luca Marchetti: and finally, I also mentioned that some exotic form of monitor can emerge from purely quantum guard effects as a result of interaction. So there's a still some work to do, even at the units level, because, first of all, we need to extend the 100 is for generic fluids, and that's that could be a key step in order to identify one of these results, actually
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Luca Marchetti: universal, not whether some differences appeared between various models. Another point that I mentioned before
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Luca Marchetti: was that and I the the modifications that we found for some particular kinds of interactions at late times, if they were there at 30 times as well, they could provide the quantum gravity purely contemporary writing mechanism for inflationary physics
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Luca Marchetti: instead a late time. So another condition that we found out was that we needed this running, this emergent coupling to actually run with time. And this is something that has been found in the in the savings of the Us. We suggested rather the same exact way, you know, cent to it. Safety
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Luca Marchetti: and running on this coupling is, in fact, the same, because it's actually the one that you would naively suggest. We wouldn't I you to guess by just looking at the dimensional is from a
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Luca Marchetti: so it might be interesting. I need to connect to safety, or to see if there's some insights from the theories that we can learn from this, at least in the in the emergent cosmological sector.
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Luca Marchetti: And then there's a question of of consistency. and which is until which time we can actually rely on this meeting field approximation. because we know on this meeting the approximation is gonna break down eventually.
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Luca Marchetti: and when the approximation breaks down we'll kind of other ways to start the dynamics. We are
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Luca Marchetti: at the level of the you know. What we've shown is that for a supervisor modes in the April model
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Luca Marchetti: we found that the dynamics of the Supervisor modes daily times. if it's from that of any. and from that that we would obtain by perturbation the background
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Luca Marchetti: we we were actually able to match the perturbation dynamics for the volume with that of Gr. And the most important physical insight that we got from this is that discover participations are associated to one of operations
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Luca Marchetti: really suggesting that yeah, that in order to you really need the some.
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Luca Marchetti: So there's at this level there's a lot of work to do so. It's 30 times. As I said, we found this mismatch with the modified gravity, and we
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Luca Marchetti: and one reason why that mismatch might be, there
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Luca Marchetti: is that, in fact, when we're trying to study the dynamics in the fiber, Id or by, we just the the background dynamics. What we do is we're essentially perturbing this case.
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Luca Marchetti: but the skate factor from the perspective of the full it's, in fact, a 0 point. Again.
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Luca Marchetti: so it is likely that the reason for this mismatch is really because the the fundamental quantities from the quantum variety perspective, and from the effective, if you want to. If I, growing the perspective, I, in fact, completely different.
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Luca Marchetti: So this might create different dynamical ones, different between the
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Luca Marchetti: and at late times instead. 1 point that that I want to remark is that in order to match you, are we needed to impose some matching conditions that were particularly out for, because they constrained completely all the dynamical freedom that we had.
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Luca Marchetti: But it will be extremely important to characterize precisely these matching conditions in physical terms, because they could lead us in better understanding what kind of group. 50 or systems have the chance to actually be related to continuing dramatic physics.
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Luca Marchetti: and of course it will be important in both of the late times to repeat the I. This for scalp reservations, possibly by using the effective description, is something that people are already working on
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Luca Marchetti: there. Of course there's a question of universality, and which perhaps could be addressed by again including for more, on to exploits and extending their eyes, is most important to you, to vector in terms of modes.
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Luca Marchetti: which is something quite complicated to do for which we need more, and some stuff in this direction has been in this paper here.
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Luca Marchetti: but still a really at this level we could be able to to study on some initial pro spectrum by for quantizing the early times that we've obtained, of course, keeping in mind that the ideal step will be to derive completely from from from gravity without having to again for on ties.
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Luca Marchetti: But if we are able to understand that then we could also be able to understand how this
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Luca Marchetti: And then, of course, there's the question of a consistency that I mentioned before of how the interactions eventually will change the picture or not. Okay, so that's all I wanted to say. Thank you all for your attention. Please feel free to ask any questions
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Ivan Agullo: and questions for Luca.
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simone: Maybe I have a question about this last point you
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raised
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simone: There's always the
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simone: a question about the physical interpretation of the traveling constant of the group in theory, or the many coupling constants. If you have multiple vertices.
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simone: and so
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simone: do you think that when you study the the we did, the interactions really change the picture. This will allow you to get some
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simone: intuition about the physical meaning of this coupling constants, and the If you have already some expectations that you want to share.
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Luca Marchetti: That would be exactly the the principle. So the idea would be to look at what what are the observable implications for in including interactions, or including even different kind of observable?
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Luca Marchetti: I look at what are the physical interpretations for those by looking at the the the microscopic physics.
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Luca Marchetti: and at that level, perhaps that's gain some more intuition about the the microscopic, the the only tuition that we have right now
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Luca Marchetti: is that the microscopic parameters turn out to be some combination of the microscopic parameters. But for now, at least, in this simple systems, which are really simple and with very simple observables.
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Luca Marchetti: The map doesn't seem to be one to one that in in one microscopy to one microscopic observer will contribute to more than one microscope.
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Luca Marchetti: But perhaps, considering again more observable sort of different kind of fields, and like making the physics of the system richer and richer, perhaps we can really gain more control or more, have more physical understanding of this microscopic couple.
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Ivan Agullo: Model.
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Mateo Pascual: Hi! Hello!
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Mateo Pascual: Just a small Clive regulatory question on Slide 4. I think it is that you
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Mateo Pascual: you right that the scalar field Kai.
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Mateo Pascual: it is valued in our deal.
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Mateo Pascual: Just a wondering what deal is. Why it's not the
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Luca Marchetti: Yeah, maybe I should have clarified that. So this is not just one's kind of field. These are Dl's profits. So one can feel this value in our.
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Luca Marchetti: So, if you have a number of them, you will need to enlarge the the the domain of the field, you know, to the to account for all this new real value, the the user freedom.
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Mateo Pascual: Okay, I see, I see. Thank you
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Luca Marchetti: definitely.
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Ivan Agullo: Panelists.
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Daniele Oriti: Yes, concerning the interpretation of the coupling constant. So
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Daniele Oriti: So I mean as as as Lucas said, the
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Daniele Oriti: if full control requires it. We compute more observables, and we have a a control over richer, effective dynamics. So far we can say the following: that okay in the the the coupling, the mass, like term in the in the free part, in the quadratic part.
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Daniele Oriti: as Lucas showed the becomes a related to the effective Newton constant in the semi-classical regime. But on the other hand he mentioned the work on this effective phantom dark energy.
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Daniele Oriti: And that's basically the statement that when you compute the effect of the interactions you can reproduce, you can you find quite genetically, in fact, an accelerated phase at late times.
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Daniele Oriti: and as a far as development along those lines with the with some kind, we find that you find an asymptotic. This interface
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Daniele Oriti: with the value of the you know. Effective late talk.
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Daniele Oriti: Sorry late time, cosmological constant. In this interface being a function of the coupling of the sixth order.
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Daniele Oriti: order, 6 interaction.
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Daniele Oriti: and some of those State dependent conserved quantities in particular queue.
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Daniele Oriti: So the emerging couple at the emerging cause Module constant, is related to one of the couplings of the interactions in the Gft action.
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Daniele Oriti: But it's a is a very simple phenomenological.
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Daniele Oriti: The dynamics for the interactions. So what Lucas said stands through that we need a much more
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Daniele Oriti: erez agmoni, you know, durable some control over the dynamics. But this is already very nice, and and if I understand correctly giving an alternative picture to the 101
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simone: quantum deformation. Origin of the cosmological Constant.
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Daniele Oriti: Sure.
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simone: Thank you.
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So
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Ivan Agullo: that's this cosmological constant. It it stays forever or or so. As I said, the dynamics is just given by this very simple type of interactions we considered.
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Daniele Oriti: which depend on you on the modulus. They only depend on 2 of the modes. So that's why it's a phenomenological type. Approach
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Daniele Oriti: within this simple model. Your the 6 interactions are the dominant ones. and at late times they you get asymptotically at this interface.
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Daniele Oriti: And so in this sense, Yes, it. You have a fountain like behavior before. But then, as you talk equally, you go to a constant cosmological, constant. and just in total value you get is, as I said, it's, a function of the the coupling constant to the sixth order interaction, and the some State dependent parameters
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Daniele Oriti: which you expect to be order one. But well.
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Daniele Oriti: we have few constraints on what the actual value, they they should have.
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Luca Marchetti: The comment on this, maybe, is that if it stays forever it's not entirely clear, because we we we have found this result by relying on the mean feed approximation, and eventually that approximation will break down.
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Luca Marchetti: So we will have to understand exactly how to go beyond, if it's approximation, to be sure, about what happens even later in later time. So if it stays forever, or something else goes on.
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Daniele Oriti: and for the same reason, because we derive the result in the mean field approximation all the numerical values of the couplings in particular, the sixth order top. And even if the form of the interaction was to stay the same beyond the mean field approximation. You would expect all of this to be renormalized.
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Daniele Oriti: so the the the very least that the quantum corrections will change the numerical value of this constants. But
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Daniele Oriti: the statement was what I what they said.
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Western: It's a question from Western or it's it's. It's question comment on this. I'm. A bit confused on this part in a look of control as well as the
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Western: So when I was
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Western: because of the kind of notification that you take in in a derive in equations that are similar to the one and all the of the and then yes, I expect to have a inflation period as well.
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Western: But then I, if I understood correctly, you're saying something else than you did that. So you are. You have a behavior that's different from the one on the because these prices, so the it accelerating time and space, and at the later time, and you have a constant period there
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Western: is. Is this correct?
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Daniele Oriti: If the question is to me, then I was referring to a late time acceleration that is produced by the interactions
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Daniele Oriti: at early time so close to the bounce. So you have something similar. I need to look pumpkin because model do you have a bounce? So you have an accelerated the phase right after the bounce. But, as Luca said, is very short-lived.
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Western: Yeah. So yeah, yeah, okay, so my my question was a comparison with so you. You are saying that
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Western: the short acceleration here at the bounce is the same as the same. Sure, we have to be okay. Yes.
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Daniele Oriti: What what I was referring to is a late time when the interactions are necessarily become dominant.
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Daniele Oriti: then you find that what they produce is an accelerated expansion.
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Daniele Oriti: and depending on the details of the of the interaction, so they can have the behavior that Lucas head of a fountain like
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Daniele Oriti: dark energy and asymptotically become a the sitter like geometry.
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Ivan Agullo: Yeah, look, I I was wondering about the the initial conditions for perturbations. Can you say something about it?
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Luca Marchetti: Yeah, I mean, for now we the only thing that we did was to compare it to the
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Luca Marchetti: with the so we do not look at the initial conditions.
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Luca Marchetti: The next step that we would like to take. Once we completely understand all the various details of the derivation, even for earlier times, would be to write these dynamics, to try to write it explicitly at 30 times. So, because this is only true for late times.
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Luca Marchetti: in order to look for our initial condition, we would have to go to earlier times.
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Luca Marchetti: And perhaps yeah, do that possibly by including a scarfield with an an appropriate potential. And at that point we could for quantize the the resulting dynamics for this carbon emissions and see what comes back to me provides us with.
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Luca Marchetti: So that will be the that will be the plan, for now we just have the late time result.
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Luca Marchetti: We we now have to explore the early times, and and understand exactly all the details of this late time. So
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Ivan Agullo: that's but I I thought that you don't want to focus on that.
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Luca Marchetti: Sorry
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Luca Marchetti: I thought that you said that you don't want to fork quantize. I I mean, I I don't want to. I I would be happier if I were able to to find this this the area of initial conditions already from the full quantum. But that is
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Luca Marchetti: so. 1 1 point you made, and I think it's very important
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Luca Marchetti: is that in order to talk about quantum fluctuations from the full contemporary theory. You'll have to construct rational observables already from the full.
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Luca Marchetti: and at at least from the from the group side of the story. And right now our the the best way we know to the most physically sounding way we know about to construct the relational observable is by using this
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Luca Marchetti: this coins, pick it states so. But this is just an effective notion of of of relationality. So we need to look more in detail at the construction operational observable. So in general in go through the perhaps using the opms and and and this kind of
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Luca Marchetti: ideas about quantum measurements that that can be imported in a, in, in, because they don't rely on on a on some notion of continuum at all.
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Luca Marchetti: So that's that's an important step that one would have to take if you if one wanted to try to study the behavior of this of these observable. So even at a time since, study the quantum fluctuations of these.
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Luca Marchetti: because right now everything is is written in terms of expectation. But so it's just the expectation volume, the Zoom Phone. So it is. Yeah, and that's through the observation. It's petition. Why, that you recover some rationality.
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Ivan Agullo: Okay, so that's that's the first step that I would say, in order to do that.
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Ivan Agullo: I understand. And one more question. You also mentioned briefly tensor and vector perturbations.
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Ivan Agullo: And do you spec and that this quantum, whatever it effects? I'm gonna introduce effective couplings between different types of perturbations, or
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Luca Marchetti: I I don't know but I would actually so, because when we started supervising dynamic to 3 times.
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Luca Marchetti: it was extremely complicated, because I said it doesn't matter anymore. If I go to the so it it might as well. Something like this might as well happen.
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Luca Marchetti: I don't know, but I would expect that it's not gonna be. It's gonna not gonna be particularly nice. So the some this kind of couplings might appear, and and that's put up very important for all of your responses. Yeah.
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Ivan Agullo: Any other question for Luca?
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Ivan Agullo: If not, thank you for the very interesting talk.
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Luca Marchetti: Thank you guys.
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Ivan Agullo: Not by under my
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Luca Marchetti: right.