Jorge Pullin: Okay. So our speaker today is Alexandra Pitts will speak about inflationary phenomenology from plank and discreteness.
Alejandro PEREZ: Okay, thank you. Car. Here. Thank you. I'd like to thank the organizers for giving me the opportunity to give this seminar, and I also like to especially thank
Alejandro PEREZ: for for maintaining this seminar over
Alejandro PEREZ: all right. So today I like to tell you about some recent work I done with my Phd. Student about that on Monday,
Alejandro PEREZ: and it has to do with the
Alejandro PEREZ: the construction of an inflationary model that naturally erased arises from the you know, thinking about possible implications of one of the main predictions of the quantum gravity, which is that of these.
Alejandro PEREZ: So I am using my tablet, and so I should be able to write on top of the slides
Alejandro PEREZ: uh, so which will allow me to, you know, interact with you more easily, I hope.
Alejandro PEREZ: All right. So
Alejandro PEREZ: general relativity is, the classical theory is expected to arise. But
Alejandro PEREZ: in the continuum
Alejandro PEREZ: as an effective effective description of something of some reality that is actually discrete at the fundamental level.
Alejandro PEREZ: And so one could draw the parallel between theory of general relativity and some other equations in which we describe physics that is fundamentally discrete in terms of continuous. Mathematics, for example, the physics of nine-year-olds.
Alejandro PEREZ: And so we know that these effective descriptions are all the true to some extent, and that they break down when one approaches the the fundamental scale in the case of now your stocks theory, or in the case of you know, physics of of ah condense matter, physics and physics of
Alejandro PEREZ: of ah matter in general. We know that this underlying atomistic nature of matter produces a lot of interesting phenomenology at scales which are much larger than the particular scales of the atoms,
Alejandro PEREZ: such as diffusion round in motion, et cetera.
Alejandro PEREZ: So the question I would like to ask is, whether we can produce a thinking by analogy, whether we can produce some interesting phenomenology phenomenology accessible to us.
Alejandro PEREZ: So, and this is part of our basic introduction. I have to. I think I feel I have to mention. This is part of the history of the subject in in our little team, you know. Thinking about.
Jorge Pullin: Yes, all right. So the problem of vacuum contributions to dark energy is the problem of quantum gravity.
Alejandro PEREZ: I I was saying. And so how is it that you know the vacuum fluctuations actually gravitate? And so already from the perspective of an effective theory, you see that there is a very simple choice which I want to emphasize because it plays a role in one initial aspect of the model I want to talk about,
Alejandro PEREZ: even though it's not going to be the central team of this talk I want to talk about,
Alejandro PEREZ: or this. This modification of the field is slight modification of general relativity, introduced by Einstein in one thousand nine hundred and nineteen, which is called einstein in one thousand nine hundred and ninety, which uses only the trace-free functions,
Alejandro PEREZ: and that
Alejandro PEREZ: when supplemented by the assumption that energy momentum is conserved is basically equivalent to general relativity up to one detail, because logical constant appears as a constant of integration,
Alejandro PEREZ: so the cosmological constant is to be provided as one more initial data, for
Alejandro PEREZ: it is not a fundamental function.
Alejandro PEREZ: In addition, the energy, the vacuum contribution to the energy momentum tensor does not contribute to the field equations, because it's
Alejandro PEREZ: because the trace part of the environment in tensor does not enter the field equation. So it resolves. So in minimal gravity. Vacuum energy simply does not gravitate. And so it eliminates in one's problem.
Alejandro PEREZ: I believe that the problem remains in the sense that one has to provide this initial data for the cosmological, constant.
Alejandro PEREZ: And if we think of a cosmological model where the universe starts at the Big Bang,
Alejandro PEREZ: it seems one can argue that it would still be natural to have a very large value, and strange or unnatural, to have the small value that we actually observe. So that constant of integration map from a natural point of view is still
Alejandro PEREZ: so. Animal reality is constructed from these two ingredients: trace fiance's, equations and the conservation of the momentum tensor. So if we drop one of the ingredients. Then we get a natural generalization of gravity as an open system,
Alejandro PEREZ: and this idea ah has been used in in something, I will say, which is briefly mentioned now. But before getting there, let me just remind you of the structure of the action principle of animal, the gravity, the action. Things for minimal gravity is just the
Alejandro PEREZ: not supposed to fluctuate that is provided from it's A. It's a background volume, strategy
Abhay Vasant Ashtekar: that when you write the action in terms of you know, the metric and the determinant of the metric. It takes this form:
Alejandro PEREZ: The field equations that follow from There are these: trace three anxiety equations, and one can try to repeat the usual argument That shows that Well, here is the matter happening,
Alejandro PEREZ: and the volume to be seven different markets means one gets a weaker condition on energy momentum conservation, namely, one gets that energy momentum
Alejandro PEREZ: erez agmoni might not be conserved, and this current of energy momentum violation. The only thing we get from an invariance, and according to serving different organisms, is that this currently has to be closed,
Alejandro PEREZ: the one as the one for
Alejandro PEREZ: And one can one can see that the type of diplomorphisms that one is actually breaking which are those that have a non-zero um expansion, those that actually, though those decemorphisms that are being broken by the action of animal like gravity, I. One point corresponding to with infinitesimal
Alejandro PEREZ: and scale transformations.
Alejandro PEREZ: And so It is this breaking of scaling variance of this um of the of the underlying volume structure which
Alejandro PEREZ: structure of any one, and if we think that
Alejandro PEREZ: but the fundamental scale. There should be something like a preferred granularity of space-time that would provide a preferred volume. Structure. In an effective description, then minimal gravity would arise naturally, and this is something that has been emphasized long time ago by Anderson and feature shine
Alejandro PEREZ: so anymore, and gravity. And this is still part of the introduction. It's something we should not be too afraid of. It's very close to general relativity, and it arises naturally.
Alejandro PEREZ: In fact, this is the effective description that arises from the thermodynamical argument of Jacobson, and it is also the
Alejandro PEREZ: so in minimal gravity. Different organisms are broken down to one hundred and seventy different artisans, because from the perspective of a more fundamental theory, we are thinking of some preferred granular structure that actually provides a measure for
Alejandro PEREZ: um. One can actually see that in one computer unimaginable, it arises naturally when one considers the normalization of the biomimicry tensor, and that, indeed, the famous um Trace anomaly that appears the great scaling values we one considers
Alejandro PEREZ: seen as a four-volume Uh, I normally bray, taking different orphans a mean variance down to volume to serving different mechanisms. So there is already a very simple and well known uh context, in which immoral gravity arises already because of anomalies.
Alejandro PEREZ: So and, as I said, minimal and gravity is nice, because vacuum flavor is going to gravitate, spoiler out by one word, and apart from Tiny from difference, happening only in the
Alejandro PEREZ: the dark energy sector unimole. A gravity is equivalent to generative.
Alejandro PEREZ: But as soon as we enter into the main part of the talk you can see what is this aspect, and from there on everything that they will say can actually be equally said in terms of general relativity or in terms of the change of language.
Alejandro PEREZ: That's all.
Alejandro PEREZ: Okay, So the question we are asking, Can we produce phenomenology from the tank and the sweetness
Alejandro PEREZ: predicted by quantity-gravity by no one in reality? And so One One aspect that I want to mention is that I believe that it opens. That the speak was discovered by the quantity. Gravity often is a very interesting channel for the possible resolution of Black Co. Evaporation and talking information, parcel and Radical evaporation.
Alejandro PEREZ: Um, and that's all i'm going to mention here. Essentially, I mean uh these. These pretty big use of freedoms can be a rich reservoir of the recent fields that purify the occupation at the end of our operation, and so maintain Unitarity in a very natural passion.
Alejandro PEREZ: And if that would happen, then the energy, conservation, or diversions of team with zero or or effective description might fail simply because some of the energy is flowing into some of the user fields that are not being accounted for in our continuous specific.
Alejandro PEREZ: And so what happens if if this is a case, or here in this few equations, we we see what minimal gravity actually predicts. So these are the trace three ancient equations. We written in this form so that I can identify the I strain tensor here. Now you use the
Alejandro PEREZ: you obtain this effective formulation of the gravitational theory,
Alejandro PEREZ: feed it by the current of energy, momentism, violation. So if energy flows from your mandate into this microscopic structure, then ah, um! The the dark energy component of the effect the evangelist equations will grow. That would be an endothermic ah process. If energy it flows from the microscopic structure into mother, the user fields. Then we will have an extra term
Alejandro PEREZ: in which, because magical, Constant goes down.
Abhay Vasant Ashtekar: What is L.
Alejandro PEREZ: Ah, sorry, Yes, and it's just so. We are integrating one form along a path in space-time from some arbitrary reference point to wherever we are, and because of the the conditions the choice of this path is, it's not valuable.
Alejandro PEREZ: So it's the path along which we are integrating. The one form
Alejandro PEREZ: All right, so and so one would like to come up with a model of how is it that this diffusion might take place? And for that we try to think about what we first the main prediction of quantum mechanics structure. But what we have learned
Alejandro PEREZ: over the years is that we cannot really think of this, as some, you know,
Alejandro PEREZ: lattice fixed lattice somewhere. But violating God is the violence; because if you violate Lawrence in violence, there is a preferred frame respect to which this structure is addressed. Then Lawrence, in one
Alejandro PEREZ: Lawrence, violating. The terms are generated by loop corrections in effective feed theories, and they become out of control. They produce your ins violating contributions, generically speaking, that are way too large, and that we not observe,
Alejandro PEREZ: describe the geometry at the quantum level. But we need to use a relational approach where the lack of survivors are the ones that are actually sent is not,
Alejandro PEREZ: but only in situations where curvature is important,
Alejandro PEREZ: and this cartoon here is supposed to reflect this intuition. So Imagine a certain three-dimensional surface made of times in regions where the surface is flat. Then you don't actually it's harder to detect the presence of the tires. But when you have curvature, then the edges of ties become more fun,
Alejandro PEREZ: and so one could actually have
Alejandro PEREZ: known as violating effects which are
Alejandro PEREZ: modulated by curvature, and then the contributions in the effective theory would also be motivated by curvature; and the fact that we don't, observe this
Alejandro PEREZ: so and again, this idea of what We' is is actually what is the true nature of the scripted by the continuity. We We all believe that the we of thing at the cinematical level is something that somehow people in areas, et cetera will have to remain.
Alejandro PEREZ: And so the cartoon for that idea is that you know the usual cartoon of what geometry and the convenient level actually means in general relativity. And we should remember that the metric, you know the suffers of all sorts of ambiguities, and the diplomatic is something that we only can define if we have a private products. So this is one of these in the years or
Alejandro PEREZ: and and space-time geometry with clocks and robots
Alejandro PEREZ: erez agmoni. And so, if you think of matter testing or interacting with this general structure, then naturally we are led to the idea that scaling violence, breaking the use of freedom are those which actually carry with themselves one hundred and fifty.
Alejandro PEREZ: The rest frame of a photon, a massless video of freedom that is scaling running cannot define a preferred rest frame. However, if I have a massive excitation
Alejandro PEREZ: of some field that breaks in invariance, then we could define the plan, scale, or on the scale of granularity in respect to that particular ah frame. This is the way in which mass Ah appears in in our field theories when we say, Ah!
Alejandro PEREZ: How can some object carry it? Some field, some degree of film carriers in such as the mask this would be, I mean, I say, in conflict with Dorothy's invalid way, way, way in the action of of massive fields, and it has an interpretation of the rest marks of the mass, or in energy in the preferred frame the frame.
Alejandro PEREZ: With respect to the excitations,
Lee: questions
it's
Lee: yes uh
Lee: in class no general relativity. When we describe cosmology, we're not. We're not unhappy that all the cosmological solutions break Lorentz and have preferred trends. Why should we be unhappy? If that was the case in quantum cosmology.
Alejandro PEREZ: The problem, I mean the No. We shouldn't be unhappy with breaking the currency variance at large scales. But if there is some fundamental breaking at the planet scale
Alejandro PEREZ: prefer frame at the plank scale, Then this argument,
Lee: and then I we will find, you know we will find in our experiments at Cern
Alejandro PEREZ: that they depend on this preferred frame, and and that's what we don't actually find. Of course, in large fields.
Lee: It's it's a start of a conversation.
Alejandro PEREZ: All right, so so an example. So I I was saying all these things because we are trying to. I am trying to.
Alejandro PEREZ: And so, because the dark energy component actually grows. I will call this endothermic case because the
Alejandro PEREZ: and I don't want to go into much much details. I just want to mention that
Alejandro PEREZ: Bye,
Alejandro PEREZ: considering these ideas about what is, what are the degrees of freedom that actually naturally interact with the animal structure, And one can actually parametrize, using essentially dimensional analysis
Alejandro PEREZ: where one shows that actually, when one has that actually only the least of those breaking steel lines are actually,
Alejandro PEREZ: we're in assuming the validity of the standard model where we're all of the relevant degrees of freedoms that are excited are massless, and therefore scaling. Are you
Alejandro PEREZ: so? The current? The process of diffusion starts when the use of films which actually violate massive laser films are first born here at the electronic transition,
Alejandro PEREZ: and with this problem that has only one free parameter that I should have written here. There is a parameter alpha i'm going to call it,
Alejandro PEREZ: for a parameter gamma of, or the parameter Gamma parametrizes our model, and for Gamma, or the one one can show that this model actually produces a cosmological constant, which is of the order of what we observe. If very, if we assume that initially, this constant of integration that I talked about before
Alejandro PEREZ: actually vanishes.
Alejandro PEREZ: Yes,
Eugenio Bianchi: yeah, yeah. The question is about
Eugenio Bianchi: a thirty fifth theory, if you can you,
Eugenio Bianchi: because then you can strongly argue that this is not just one proposal, but it's the most general proposal. It has just one parameter
Alejandro PEREZ: I'm. Considering the particle, excitation and and and looking at what would be the most general friction type force that we get right for the propagation of the particle. So we are not even in the field. There is no framework, but rather considering the particle
Alejandro PEREZ: um
Alejandro PEREZ: that the force has to depend intrinsically from the division of the particle. Only so
Alejandro PEREZ: so I can I. I can show you more more details. All the details are in the papers. We try to produce a feel theoretical version of this, and so we have some partial success, but nothing that we have uh, but not complete. I mean. Everything becomes much harder when you want to
Alejandro PEREZ: much harder at least to me. You know, when you want to consider quantum theory as an open system. And so I would say that this is working progress
Eugenio Bianchi: I see. So this is on the side of team, you know. It's models particle models for union, but that the way back reacts the way it couples to gravity.
The
Eugenio Bianchi: Yeah, It sounds still like an F two, or it is an for a number of derivatives up to two.
Eugenio Bianchi: So ah, this J. Depends on the on the mean field geometry. So they are not the the field equations. Are these ones with this J. Even from the outside.
Eugenio Bianchi: I don't want to leave it like me, The model.
Eugenio Bianchi: Okay,
Eugenio Bianchi: Thank you.
All right.
I mean,
Abhay Vasant Ashtekar: Eugenia was talking about divergence. But
Abhay Vasant Ashtekar: this, this, this is this classical in that I'm: going to.
Abhay Vasant Ashtekar: Okay. So it
Abhay Vasant Ashtekar: Yeah,
Alejandro PEREZ: All right. So just one last thing about this, which is still part of the interaction.
Alejandro PEREZ: The thing is that this friction effect on this current is, I mean, introduces a Lorentz violation
Alejandro PEREZ: into the game, because on energy, so the effect would be proportional to you know the co-moving time. Um Spectro field. Not surprisingly. I mean this is the Lawrence frame that is selected by the Fw. Solution that we was referring to,
Alejandro PEREZ: and the force or the divergence, I mean the force, the friction force. It produces tolerance, violation
here. This this um.
Alejandro PEREZ: So this is why we said that these ah operators are. But when you look at the you know dimension for the dangerous operators dimensions, or and lower. You don't find many things that you can write, because because the curvature is there, and so the ones you can define
Alejandro PEREZ: are just so suppressed by the scalar curvature in normal situations,
Alejandro PEREZ: that this Lawrence violating terms would pass all the tests that we know that look for Lawrence, violation in volatility.
Alejandro PEREZ: All right, So these ends, these are all things. And this ends the introduction kind of because I one more
Alejandro PEREZ: interactions with matter. It could also decay
Alejandro PEREZ: an exotic process where energy actually in matter, degrees of freedom is produced.
Alejandro PEREZ: And ah! And this is a possibility that it's allowed out by unimole the gravity, and that's the only thing, we the only aspect we're doing, All the gravity and the whole discussion that you have given at the beginning is important for the rest of the talk.
Alejandro PEREZ: So if you want um, just keep in mind in molecules for a few more or one more slide, perhaps, and then we can forget about it, because the rest of the discussion does not completely completely be praised in terms of generative.
It's a
Alejandro PEREZ: the the thing I want to.
Alejandro PEREZ: So this is an input of what comes next. We're going to assume that the universe starts with the cosmological constant of the order of blank scale, and that it decays in an exponential way with respect to some natural time variable
Alejandro PEREZ: in cosmology, which is associated to four volume time. So we will assume that the cosmological, constant decays exponentially in four volume time.
Alejandro PEREZ: The inflation and the main difference is that from the very beginning the
Alejandro PEREZ: unsettled conceptual discussions here. The point of view is that at the plank scale in blue quantum gravity, for example.
Alejandro PEREZ: So these are all words. Now, i'm going to try to give you more details about the construction of this model.
Alejandro PEREZ: Right? So, as I said, we postulate because vertical, constant to start off at the
Alejandro PEREZ: the natural planks scale into the cave
Alejandro PEREZ: exponentially with some
Alejandro PEREZ: in a time. T.
Alejandro PEREZ: Which is this preferred time of minimal gravity. In the context of cosmology,
Alejandro PEREZ: then something that decays exponentially in you of all time. You
Alejandro PEREZ: the case very slowly, if Beta is sufficiently small in terms of the scale factor. So if you look at this formula, it
Alejandro PEREZ: you know the postulated exponential decay.
Alejandro PEREZ: Uh, you know, if we think of an analogy of a radioactive er decay, or that you know the natural granular structure that is allowing this energy to flow from the grains to matter. The use of field
Alejandro PEREZ: is defined by this preferred volume, structure of universal gravity. The
Alejandro PEREZ: looks like this one. So you have a very slow decay, and when you
Alejandro PEREZ: so here it is explicitly written in terms of the scale factor. When the argument of this exponential becomes order one, then you have an extremely sudden transition, in which the cosmological constant drops.
Abhay Vasant Ashtekar: So at this stage there is no matter at all. Is that right? And this is go smaller than a constant. But there's no other matter.
Alejandro PEREZ: Yeah, there has to be matter to use a freedom because because
Alejandro PEREZ: because of this equation. So if the cosmological constant is actually decaying, it is at the cost of producing energy into the matter.
Abhay Vasant Ashtekar: So for this, for what I mean, I mean, like the matter of that kind of freedom and robbers and Walker.
Abhay Vasant Ashtekar: Yeah, scare the field or dust, or whatever it is. Is there a matter like that, or is this matter, or they create any?
Abhay Vasant Ashtekar: And so this is all. Sh me that at this, at the plant scale, then it started model matter what? What scale is a standard one?
Abhay Vasant Ashtekar: Okay, I'll actually plant scale, right? Because we start the Dk there. So it must be at the until the plants get that.
Abhay Vasant Ashtekar: Yes, but because we are doing some.
Alejandro PEREZ: Yeah, I would say I I think it will write it explicitly in the next slide.
Alejandro PEREZ: But the important thing I want you to realize here is that the cosmological constant is basically constant until it drops suddenly at some
Ivan Agullo: number of defaults that we call an end. So basically beta can be trained with is an end.
Alejandro PEREZ: Okay, so how many efforts you want to have? It depends on how small this is. So you can actually express things in terms of this number of defaults or in terms of Beta. Yes,
Ivan Agullo: it was. You are a gill. I I was asking something that you are explaining now. So forget about it.
Laurent Freidel: Okay, I do have. I do have a question uh,
Laurent Freidel: and you know,
Laurent Freidel: So it's because if the matter is the usual matter, then it's energy, momentum, cancer is conserved. But then, you
Laurent Freidel: that so? You want to change the conservation of energy, and you know momentum, so then
Alejandro PEREZ: it it wouldn't be conserved if I mean it's only conserved in a context where space-time is smooth to all scales.
Laurent Freidel: But i'm saying, when you say you're taking the stand out. Model matter. The the energy momentum tensor of standard. Mother is conserved right.
Alejandro PEREZ: It wouldn't be conserved if it's coupled
Alejandro PEREZ: with this underlying granular.
Laurent Freidel: Okay, But yeah, okay, that was my understanding. Like your model, I mean, before you ask for this greatness requires the energy moment of tensor to not be concerned, right? So So that means you're you're really proposing a modification of the usual startup equations of States.
Alejandro PEREZ: Yeah. Yeah.
Alejandro PEREZ: I mean, I believe that this question is really homogeneous questions. So if ah, I mean full understanding of this mechanism, will require to actually describe in detail what is the coupling of the smooth or low energy, the use of freedom of our matter, theories
Alejandro PEREZ: with
Alejandro PEREZ: the quantum geometry, the use of them, which is what we are all trying to do It's just that. It's hard, and I am jumping ahead and saying, Look, this is a possibility.
Alejandro PEREZ: Okay, like, you know, like um.
Alejandro PEREZ: Then in one, two field or one to fifteen in special relativity or just classical field theory and special relativity, energy momentum is conserved. Then you can find that a stronger statement that if you define it, reach you, the energy that goes into the
Alejandro PEREZ: that. The reason is that muttered use of films can work into gravitational fields and produce gravitational waves. So this is a very rich phenomenological discovery, right? The systems are initial weight. What I'm saying is that at the ultra violet it could be another channel for energy to be lost into something else.
Okay,
Alejandro PEREZ: which has to do with the fact that our space-time being smooth and to all scales is only an approximation.
Laurent Freidel: I mean, I miss the connection. So I understand that there's an assumption here. You want to change the questions of state by conservation I mean D Atb. Equals zero right conservation of the energy
Laurent Freidel: which you know mean only conservation of energy, if there's kidding, but it's it's a bit more general than that,
Alejandro PEREZ: you're changing. You're relaxing that condition by having a right-hand side
Alejandro PEREZ: a of all this. Right?
Laurent Freidel: Yeah, Yeah, they Are you talking about?
Laurent Freidel: Yeah. And you're saying that the
Alejandro PEREZ: you need to add all the ideas of fields that interact with electric and magnetic fields to have a diversions free. So
Alejandro PEREZ: So if you want What I'm just saying is that there's a non-trivial interaction between matter, the use of films and our energy, that's all.
Laurent Freidel: But the question that was is. You seem to assume that this source here for the eighteen Union is not zero is planck in, but it could be valid in right. So
Laurent Freidel: is that is that your assumption, or
Alejandro PEREZ: is on a mechanical. But I don't see the argument why it has to be.
Alejandro PEREZ: I am saying that if There is an environment that is discreet then, and a profit of use of films are not captured by a continuous description. Then naturally,
Alejandro PEREZ: this would produce this type of effects. Of course you could have some model of dark matter, and I believe they are.
Alejandro PEREZ: And you just postulate some interaction between the and and and this has nothing to do with quantum gravity or ganularity, and then you would have again divergence of T. Mu, not equal to zero, but equal to you know how much
Alejandro PEREZ: it would be a a generalized continuity equation that parametrizes, how energy flows from the usual metadata into that energy and vice versa in that mechanism like my money. People study this from purely phenomenological
Alejandro PEREZ: perspective, in which they, I don't know exactly what are their motivations? Sometimes you don't need calculations which is explored because it's available.
Abhay Vasant Ashtekar: But in my
Abhay Vasant Ashtekar: in my mind
it's
Abhay Vasant Ashtekar: just to clarify what is confusing me. And also, I think other people is really that you write down this equation and the previous slide, please. You just have that
Abhay Vasant Ashtekar: you write down this equation So that question implicitly, I that there is a metric.
Abhay Vasant Ashtekar: The statement is that if there is a metric,
Abhay Vasant Ashtekar: there is a metric, and if there is a metric, and if t new is really, or T. A. D. Is really the standard model, especially with respect to that metric,
Abhay Vasant Ashtekar: then it must be conserved
that diversions of the team menu of the standard model is zero.
Alejandro PEREZ: Okay, It's all in time.
Alejandro PEREZ: Okay, Yeah,
Alejandro PEREZ: All right. So. But okay, So
psingh: don't want to get stuck in this slide. I have given this.
psingh: Yeah,
psingh: Alex: I'm: sorry. Like, like. My question is exactly about this slide. So in the not in the
psingh: Yes, it grows again. So this period is when the cosmological, constant decays exponentially.
psingh: No, no, thank you for the question. But I was going to say on this. It's just that. That's what I wanted to say, I don't want to get stuck forever here, but they are very important things, I must say, Okay. But I have a following question on this. So I understand the part of row radiation going as a bar minus four on the left hand side and on the right hand side.
psingh: What I don't understand is that when you have this
psingh: uh radiation, or whatever matter is being created from this J. From this current and Dj. And then there is an increase by, and it is increasing as A. Q. Why do you call it row radiation when it doesn't act like radiation?
psingh: We know that radiation to act like radiation from the Stephen Boltzmann Law from the standard matter, and I I don't want to get into again the same confusion which I share with Abbe and Laura. But the point is that if the matter fluid is not acting like
psingh: to the power minus four, its equation of state is not W. Called one by three. So that is not radiation. That is something else. Then the
Alejandro PEREZ: I completely understand your questions. So let me answer the question you.
Alejandro PEREZ: However, it is changing with time. Therefore the process is exotterming. There is energy flowing into some the use of feelings which I so there is a coupling between fluids, the coupling between the cosmological constant. And
Alejandro PEREZ: yeah, I do have them there, and we're going to get to the questions
Alejandro PEREZ: sending energy into the radiation.
Alejandro PEREZ: Now, at the beginning
Alejandro PEREZ: the beginning.
Alejandro PEREZ: Ah, there!
Alejandro PEREZ: Okay.
Alejandro PEREZ: So at the beginning you have an exponential expansion
Alejandro PEREZ: that is so violent that, as usual, inflationary cosmology dibutes exponentially, the radiation so radiation goes like one over eight to the
Alejandro PEREZ: modify, the not the equation of sales, but the behavior of the radiation with the State factor. And so at this point, with the addition decays sufficiently so that the remaining radiation is comparable with the amount of radiation you are injecting. Then addition starts growing again, and it behaves basically like A. Q.
Alejandro PEREZ: They are Also, I mean, all this is New Mexico.
Alejandro PEREZ: We have to do a numerical calculation to actually solve the Friedman equations and the modifying calculations.
Alejandro PEREZ: However, you can just do some seminolithic approximations that actually lead to these statements that I have written in the picture.
Alejandro PEREZ: Not only that you can also show that you can calculate until when the relation goes down and up to when it goes up at the end interest. So this is Nm: This is the end of inflation. This corresponds to this moment, in which the cost of the constant decays to zero.
Eugenio Bianchi: So this well, it's somewhere in middle, and sorry. I mean the quantitative estimates are in the paper, but I don't have
Alejandro PEREZ: the typical scale has to do with with lambda dogs. Right, Lambda dots. How much energy and this has to do with Beta.
Eugenio Bianchi: All this is all. This is very clearly analyzed in the paper. If you're interested in the details. But I really have to go on because this is not going to be that important, as you will see,
Alejandro PEREZ: the radiation dilutes extremely fast, exponentially at the beginning. And then there is a reheating induced by the decay of the cosmological constant, and that this week it takes us back to something of the order of the tank, temperature or density one.
Alejandro PEREZ: But there is a source to radiation, and this source is the one that we modify the behavior of radiation with scale.
Alejandro PEREZ: So you can solve everything.
psingh: Yeah. So just just a small command. Thank you for clarifying this. But I think, like the I think most of us are probably confused, because,
psingh: uh, we always try to think back again in terms of Gr. But the interesting thing is that when you you can call it radiation. I'll probably call it something else. But the point is like in that regime where you're when you say your quote and Co. Radiation is increasing. You are actually having violation of weak energy condition. If I try to map it to the standard model of cosmology,
psingh: the equation of State acts like minus two. So
Alejandro PEREZ: it's totally not valid, because you are injecting energy into the system.
Alejandro PEREZ: It's like having it on, and you are heating up the on.
psingh: I think the problem is that probably you Won't interpret it exactly as radiation
Alejandro PEREZ: at the end. When Lambda decayed publicly, and there is no more Lambda, there is a zero here, and this, too. It behaves like one over H before
again.
psingh: Yeah, I think we should discuss discuss later. Thank you.
Okay,
Alejandro PEREZ: Well, not all of them, I mean here you suddenly reheat the universe. But the important thing is that you reheat it back to you
Alejandro PEREZ: two. Um! So you see here. Um,
Alejandro PEREZ: you see that what we find numerically it can be easily find found, and it's genetic enough so that you get basically the
Alejandro PEREZ: to order. It might use the same results with this spacing divide model.
Alejandro PEREZ: All right. So
Alejandro PEREZ: so I I have to mention something that is very important in this type of models. That uh, that was uh um, something that was raised to me in many talks, and it was always a difficult question. There are some things that people have pointed out in stabilities
Alejandro PEREZ: when when one considers an interacting that energy through it, like the one I am considering that it
Alejandro PEREZ: and collaborators show that this type of interacting that energy fluid actually does not suffer from the instability. So they are quite, you know, well known in Ah, in some areas of cosmology. And I have just used this paper here for the
Alejandro PEREZ: add that basically it has shown that these problems are not present in these like models. And this is the good news for
Alejandro PEREZ: okay, so I can go to the key thing I wanted to tell you in the talk,
Alejandro PEREZ: So we have, Therefore this model exhibits inflation for a certain number of efforts,
Alejandro PEREZ: but there is no inflex on
Alejandro PEREZ: so just a proof of concept. Is there another way of thinking about the
Alejandro PEREZ: what we see at the Cmb.
Alejandro PEREZ: The notion of homogeneity it does. It simply does not make sense in the phenomenal theorem, which is what we I think is the case in a theory like, Look on the right. We have all these effective descriptions and the cosmologies very useful to get the other nutrition.
Alejandro PEREZ: Uh this granularity that actually breaks
Alejandro PEREZ: the cosmological symmetry. So what we want to explore is a possibility that this underlying grammar structure will feel in homogeneities into our matter the use of freedom that would eventually become visible at the
Alejandro PEREZ: He's so. Ah,
Alejandro PEREZ: but again
Alejandro PEREZ: with the idea.
Alejandro PEREZ: But it's not a properly crazy assumption. People sometimes think that this could be the case. But anyhow, the main motivation here is to find
Alejandro PEREZ: a proof of concept that, given a certain context, actually these ideas actually might make sense. So we only have the standard more particle physics, and we will assume, And I think I I wrote this in a slide that I ended up invasive. We will assume that the Higgs killer, so not only none that
Alejandro PEREZ: He's basically London.
Alejandro PEREZ: My target is not
Alejandro PEREZ: again. This is not a totally crazy assumption meter in many inflationary models. The impact of the field is set up with initial conditions of a plan scale. So we're Assuming this for the Higgs scale. Now the heat scalar at those energies is the only thing that actually breaks Skinny alliance.
Alejandro PEREZ: Rather a structure you need to break scaling violence. Then there will have to be an interaction between the heats and the glorious structure.
Alejandro PEREZ: So this interaction would be ah analogous to a Brownian interaction between. You know the molecules and in, and the pollen particle. Here the analog of the molecules will be the ground on the structure of the blank scale, and the analog of the degree of freedom of pollen
Alejandro PEREZ: would be the field theoretical degrees of freedom of the Higgs, K.
Alejandro PEREZ: So this heap scalar is interacting with the granular structure, and so it inherits in homogeneities associated to the underlying homogeneity of the quantum genre,
Alejandro PEREZ: and so they would be in the motion eight is generated at the planning scale,
Alejandro PEREZ: a very typical scale, which is the time scale.
Alejandro PEREZ: But in homogeneities it's scaling.
Alejandro PEREZ: However, we would see that because of the sitter expansion,
Alejandro PEREZ: a certain approximation, because there will be violations of small violations of scaling violence, which are exactly also things We need to explain what we see at the scene
Alejandro PEREZ: erez agmoni manner. So the thing that I will not describe is the details of the quantum gravity interaction between the hits and the randomity. This is going to be described by stochastic process, so we will assume that we can describe the generation of inhomogeneities by a stochastic process.
Alejandro PEREZ: These are the fluctuations of the heap Scalar and I'm going to assume that the first moments are zero
Alejandro PEREZ: only we will only need to consider the second moments, and the second moments are included in the two-point correlation. Function.
Alejandro PEREZ: Yeah, very importantly, please keep in mind that these brackets mean ah ensemble averages in this stochastic process. So the Higgs will generate fluctuations because it's hit by the general Structural bank scale
Alejandro PEREZ: in it.
Alejandro PEREZ: Second moments will not be trivial, and they would be entirely encoded in what is called the power spectrum. So just because the process has to be homogeneous and isotropic in average. Then,
Eugenio Bianchi: so, if you know the power spectrum,
Alejandro PEREZ: you know the two-point function. If you know the two-point function, we know the power. Thank you,
Alejandro PEREZ: or you have information about the power. Space.
Alejandro PEREZ: I will answer the question in a moment
Eugenio Bianchi: at Venezuela.
Alejandro PEREZ: Okay,
Alejandro PEREZ: uh energy momentum
Alejandro PEREZ: contributions to out there the
Alejandro PEREZ: in homogeneities, Then that's a simple exercise, because the stochastic process is homogeneous and isotopic. Then what you get for this expectation value is something that that corresponds to a perfect fluid. So basically you don't get any
Abhay Vasant Ashtekar: an isotropic stresses, because, of course, this would violate isotropy. So you only get something that is an energy density, contribution, and a term that is proportional to this space like metric
Alejandro PEREZ: inflation
Alejandro PEREZ: very quickly go to zero.
Alejandro PEREZ: So now, if you have,
Alejandro PEREZ: you know the contribution,
Alejandro PEREZ: the equation of state, the one that comes from diverges of T in your equal to zero,
Alejandro PEREZ: or equal to something, because it would be the source now. But the key point I want to say is, i'm going to call this W. Perturbation. This is the world, the energy cost of producing perturbations on the scalar field.
Alejandro PEREZ: This quantity depends only on the power spectrum of
Alejandro PEREZ: perturbations of the heat scalar. So I can think of this work.
Alejandro PEREZ: Of course I have to express Delta R two, and the Delta Phi two in terms of the two point functions of the field. But these are all polymatic things in in the field, and therefore can be expressed in terms of
Alejandro PEREZ: the power spectrum.
Alejandro PEREZ: So the point now is that I want to write an equation that describes this is this stochastic process in which the Higgs is rolling down, so to say, or evolving in a in the granular
Alejandro PEREZ: geometry, and therefore being hit by this granular structure. And so this
Alejandro PEREZ: the natural way is to think that this injection, because this is happening, during which, during the time which for which the universe expands exponentially,
Alejandro PEREZ: the only natural scale around is the puddle rate at the moment. And so we postulate that this energy injection is proportional to the Hubble rate to the right power. This is just dimensional analysis where we introduce this friction provision, gamma, which is dimensions.
Alejandro PEREZ: So this parameter gamma parametrizes how much energy
Alejandro PEREZ: from dimensional reasons, and you find this powers of a in fact, if you write here. I have written the continuity equation in terms of in terms of skate factor. If you write the equation in terms of probing time, then you will get something like this
Alejandro PEREZ: in common time. We're injecting energy at a constant rate completely controlled by the geometry of the universe, which is given by the scale by the hammer. Right? So this equation implies this equation,
Alejandro PEREZ: and this would be a free parameter on our of our model.
Alejandro PEREZ: This is what this This is an example of how this quantities depend on the power spectrum,
Alejandro PEREZ: for example,
Alejandro PEREZ: because
Alejandro PEREZ: the energy density depends on the derivatives of the field, then there will be the power spectrum appearing in the needle, and the derivatives respect to space, like variables or produce K factors. And there are other things that have to only the evolution of the vacuum expectation value of the heats.
Alejandro PEREZ: Okay, So we integrate from some.
Alejandro PEREZ: So this equation that you have is
Alejandro PEREZ: because
Alejandro PEREZ: I don't know how. My, how am I doing on on time
Jorge Pullin: while you've been on for an hour and twenty minutes already?
Alejandro PEREZ: All right. Okay. So this equation is a function of the power spectrum that can be solved in this solution.
Alejandro PEREZ: So maybe, in order not not to lose you all, I see that already,
Eugenio Bianchi: Riandro at.
Eugenio Bianchi: I i'm sorry I It's very important to me to understand when where the one over two cubic is coming from. If there's a simple answer to that that will be really
Alejandro PEREZ: yes. Um
Alejandro PEREZ: um do. I have a simple answer.
Alejandro PEREZ: Ooh!
Eugenio Bianchi: We learn
Eugenio Bianchi: inflationary cosmology.
Alejandro PEREZ: It's not different. It's it's the right.
Eugenio Bianchi: Do you agree with the mechanism, it's different.
Alejandro PEREZ: Oh, yeah, yeah, the mechanism is different.
Alejandro PEREZ: That's right. Unfortunately. Now, being tired, after all this discussion, I can not tell you. It is very simple, but you have to write this equation,
Alejandro PEREZ: but I am sure I have a simpler answer, but it doesn't come to me at the moment, but it has to do the fact that you know.
Alejandro PEREZ: Well, this is not enough.
Alejandro PEREZ: He's still guaranteed, i'm.
Alejandro PEREZ: I'm sorry I don't have a simple, quite answer. But there is a simple answer. But
Alejandro PEREZ: let me think about it, and I will write to you anymore. Okay,
Eugenio Bianchi: thank you.
Ivan Agullo: Can you also include me in the email. I think this is the most important part of the talk.
Alejandro PEREZ: Okay?
Ivan Agullo: Yes, of course I can include you in the in the email. Thank you.
Alejandro PEREZ: Yeah, let me not say anything because I would say stupid things. Let me write. It may ah complete the answer to this point. If somebody else wants to know. Ah, to send me an email, so that I include you in the that that message Okay,
Alejandro PEREZ: all right. So one gets a skin invariant spectrum,
Alejandro PEREZ: you know I I keep thinking about giving you the answer. Um,
Abhay Vasant Ashtekar: Maybe Lautaro remembers the cancer. If you do, I think some of us I would like to leave in just a few minutes because of our meetings, and so on. So maybe
Alejandro PEREZ: the the heap scalar has the power spectrum which is killing variants. But now you have to. You have to solve linearized gravity equations to evolve this in homogeneities, this in homogeneities, will produce in homogeneities in the metric the,
Alejandro PEREZ: and for that you could use
Alejandro PEREZ: different methods, and to us the simplest one was to use this beautiful result by one Weinberg that some people call the Weiner Theorem
Alejandro PEREZ: today, or at the Cnb. Without knowing all the details of the Physics between the moment in which the fluctuations were generated and the Cmd.
Alejandro PEREZ: Just because of a very simple structure, general structure of linearized gravity of the Einstein's equations in the weak field approximation. So if the weak field approximation holds, then you can show that this is the way in which matter fluctuations behave
Alejandro PEREZ: with time. So you only need to know how the background evolves. And this is how the nutrient potential evolves, and the thing we measure at Cmb. Is really to this R. K. In this Rc. Is related to some neaplassion of the scale at a three dimensional scale curvature.
Alejandro PEREZ: So the thing is that you can use this result, which, by the way, we we we revisit in our in the appendix of the paper, because if you read one word it's quite complicated, and we we found a way of sending it in a little bit simple manner.
Alejandro PEREZ: So it might be interesting to look at our appendix. Of course there is absolutely nothing new in the appendix. It's just the rewriting of the result of
Alejandro PEREZ: due to its self interaction potential. And so this lambda that you see here for the first time.
Alejandro PEREZ: In fact, I should have said you saw it before, too, is actually the lambda that appears in front of the
Alejandro PEREZ: the fight to the fourth term. In the potential of the heats
Alejandro PEREZ: the deviations from scaling lines are directly tied to the self-crapping of the heaps. And so observations require the amplitude of
Alejandro PEREZ: this to be something. This is what observations
Alejandro PEREZ: the friction term that was a free parameter that we put by hand, controlling the amount of energy that is being injected into the
Alejandro PEREZ: you know, due to this friction mechanism in this stochastic process. It's not a non-natural one. It's exactly of the order of magnitude of the ratio of the mass of the heats in the gang.
Alejandro PEREZ: So these are. These are just pictures from this paper, where we, when you show, when you see that if you assume the validity of the same amount all the way to time scale. Then the self-coupling flows into minus ten to the minus two, which is the value that We require to explain the observations we can also do. In addition to computing the
Alejandro PEREZ: aviation or scale lines, we can also compute the next
Alejandro PEREZ: correction, and we find for this quantity
Alejandro PEREZ: the so the model
it's a,
Alejandro PEREZ: and so people have to be. But there's not a very nice thing about something that excited us a lot. I mean it doesn't have it. It's just an interesting idea and interesting perspective. Because this union the universe gets reheeded back to time scale.
Alejandro PEREZ: Then you find that just from the thermal distribution of the Black hole, the amount of black you can produce at reheating of the other blind scale.
Alejandro PEREZ: You can actually get about the right density for dark, matter, without a strong prime tuning. Just we have to tune a little bit. What is the mass of this remnants? Or We pre-mort your black holes, but not fine tuning, because the the smallness of things come from the exponential
Alejandro PEREZ: drop of the the Boltzmann distribution. And so so we we found this interesting. And then in a loops I really I I I found out, I mean back into Orleans, that actually this idea is something that they have put out in this paper. Here
Alejandro PEREZ: the temperature, then you have a natural generation of dark matter in terms of memorial black holes,
Alejandro PEREZ: the that would lead naturally to inflation, and with that, with natural conditions and some strong assumptions, I read
Alejandro PEREZ: the transition symmetry breaking, and you know the validity of quantum field theory at transplant and scales. Of course, here I have to assume that I can do all this semi-classical analysis all the starting from the blank scale. But I don't have to assume anything
Alejandro PEREZ: at higher spheres,
Alejandro PEREZ: so that I would. I would say that there is no transplantian problem here, even though the assumption that we can use. You know the semi-classical equations at those high scales, and it's from one.
Alejandro PEREZ: So we have deviation from scaling values that are parametrized by the self-capping of the heats. We have a prediction if you want something that has not been one pressure yet, and that the model produces the
Alejandro PEREZ: it's all.
Alejandro PEREZ: There is this idea of primitive black holes, a stark matter which Carlo and Francesca have, and others have evoked, and and Oranian has this idea of generating them from thermal equilibrium, and from thermal generation.
Alejandro PEREZ: So if also the parameter beta at the beginning, from the relaxation, notice that it does not enter any of the observable quantities we only need Beta to be sufficiently small to have a significant number of efforts, so that everything fits in the usual
Alejandro PEREZ: and the Us.
Alejandro PEREZ: Thank you for your patience, and thank you very much for your pleasure.
Jorge Pullin: Any questions left?
Jorge Pullin: I got one question here. Yeah, at a hundred. Thanks. A lot for your Obviously, it's been very, very nice. Also, I will send you an email so that you can include me in that answer. So I have a question: What happens with all these standard issues. That
Alejandro PEREZ: Um:
Alejandro PEREZ: yes. Okay. So here we do have inflation. We have a face that lasts for sixty falls about sixty falls of the
Alejandro PEREZ: of the reputation
Alejandro PEREZ: of exponential
Alejandro PEREZ: expansion. But of course we assume we
Alejandro PEREZ: I don't fully understand how this actually resolves these issues. One has to always make some sort of assumption about the degree of homogeneity that things have initially otherwise. You won't get any
Alejandro PEREZ: so here at the moment. I I don't have much more to add about that we are assuming things have to be homogeneous, and there is a topic to begin with, we don't make it. Ah, comedy! Only One thing that I can mention is that the thing is robust under the initial conditions of radiation
Alejandro PEREZ: inflation. But for the very same reasons or as inflation,
Alejandro PEREZ: it's just insensitive to
Alejandro PEREZ: so um
Alejandro PEREZ: erez agmoni. Well, if they were here initially, they would be diluted exponentially as well. A problematic aspect of this is that we have a reheating all the way to the time scale. So if you have some grand unified theory instead of the one,
Alejandro PEREZ: but I might be
Alejandro PEREZ: naive. I know.
Jorge Pullin: Okay, Western.
Western: Yeah, Thank you, Alex. Actually, your Toko was very dense. Full of things. Bit are the
Western: but just everything. So let me focus on the question on the last part where you mentioned that the production of primary public calls, and of course it's about to for any models in which I I haven't just adopted, because uh, so you form primarily calls uh after your inflationary periods, and uh,
Western: the and you form a promoter that calls to deals at the time scale. So the work that we have done regarding the stability of remnants of remnants was ready to the fact that those remnants had a very large volume inside that is new to the bay along the uh. So first I wanted to understand. Whether do they have? Do they form, indeed uh the plan scale. So without the
Western: right. So so maybe maybe this type of mechanism for stability wouldn't hold for this black hole. These are yard black, or somehow generated by by by thermal fluctuations at a time. Scale so. But but we don't know enough about tanking black holes to actually
Alejandro PEREZ: say that black holes should not be stable at those caves right? I mean. One often sees these pictures in which one rules out contributions to dark
Alejandro PEREZ: matter as from memorial black holes at the low mass of you know black holes because of hockey mediation is something that we can only trust for microscopic backgrounds. We don't really know What is the final shape of this evaporating that
Alejandro PEREZ: they could be stable because they have a large volume, as you say, or maybe they could just be stable period because of some quantum reality effect. So if you, it is so natural, I mean quantum reality comes with this
Alejandro PEREZ: Moscow.
Alejandro PEREZ: But why not? And so here. We observed that if there were such things like plank Mass:
Western: Yeah, not fair. Fair enough, I agree. But I I I like this idea of having defects going into black holes, I think uh may bring uh i'm! At least in the mind of the people. My trigger problems like the one you said for, uh, for a hokey radiation in the sense that productions of uh uh radiation. So i'm happy to discuss.
Western: Yeah, using the terminology of people, Your black hole for something that has to plan for us is not a good idea
Alejandro PEREZ: too late. The paper is written like that. But if you choose not to write it like that. Then it sounds strange for other people. I suppose
Alejandro PEREZ: these ones not yours, I mean even a black hole. If they become stable close to the bank scale. I wouldn't say that we can call these things black holes in the usual sense of
Western: Thank you.
Jorge Pullin: I'm. By
Abhay Vasant Ashtekar: so, Alex, I mean, It seems to me that this whole mechanism you don't really need standard model, I mean sort of excess baggage. I could just have a Higgs scale. Right? That's what is driving everything else. Everything else is a spectator one,
Abhay Vasant Ashtekar: but the running of the coupling is
Abhay Vasant Ashtekar: solid work over the years, and it's now considered as a serious candidate, right? That's in fact. So in on as a big inflation. So
Abhay Vasant Ashtekar: so if I take my to take that point of view, it seems to me that if I, where the Standard thinks for some things inflation, I will just say, Well, I mean I don't need to make assumptions. The plank regime. I just make assumptions, you know, in the usual
Abhay Vasant Ashtekar: minus eleven times one scale. They're usually the inflation supposed to start, and I just say that Well, everything was then done by the Sig mechanism. In fact, they get exactly all these curves right now, et cetera. Of course their input is that the field was in this burge Deb is back in, and their motivation for the ideas. Because
Abhay Vasant Ashtekar: so I think that so, if I like to compare and contrast, because there's a kind of question that people obviously so here. In some sense it is more satisfactory because you're going all the way to condemned. But then,
Abhay Vasant Ashtekar: exactly that reason you have to make all kinds of assumptions right? And so do you agree that
Abhay Vasant Ashtekar: that is, that somebody who is doing standard inflation, kind of pigs inflation might not see the advantage of doing these things.
Abhay Vasant Ashtekar: I I agree, I agree; but but people standard inflation has fifty years or so of history and inflation is not bad or
Abhay Vasant Ashtekar: no, no, but the actual formation. The mechanism for structural formation is the same as usual information.
Alejandro PEREZ: And so people
Alejandro PEREZ: I get used to some many issues there, I I would say, and so I I mean in particular, I You do make assumptions about the planning scale, and all beyond the time scale. Because this bunch Davis vacuum you have to think about. You know these modes that we see at the C. And B. Actually come from scales.
Abhay Vasant Ashtekar: The same assumption there. So it's not there.
Abhay Vasant Ashtekar: They have to.
Abhay Vasant Ashtekar: They are there below the planet scale. No, you don't understand that they are there. I mean, it is not a hawk assumption that they are not there, but your work also. There is an ad hoc assumption that you started at the fun scale, and there is nothing about.
Abhay Vasant Ashtekar: It seems to be that it
Abhay Vasant Ashtekar: I mean, I agree with you, I I it's not just to understand, so that when I people ask for question, I I I think I think this this This is just a an idea that sounds interesting to to us for many aspects, but it's just the starting thing, I mean. Maybe I mean once it's just the proof of concept is is something that shows that there is another way of getting
Abhay Vasant Ashtekar: the idea that the Cnb is ah is, is what look into reality predicts that we actually that the universe is in my microscope, that we are seeing actually the fundamental in homogeneous that we are always there.
Jorge Pullin: Can you?
Eugenio Bianchi: Yeah, thanks for that.
Eugenio Bianchi: There's a formula there in a box.
Eugenio Bianchi: Yes, this one.
Eugenio Bianchi: So you have the statement, and this one matrices observations beautifully. I don't follow all the steps of how you
Eugenio Bianchi: This is an observation. Okay, it's not.
Alejandro PEREZ: It's an observation
Eugenio Bianchi: that makes the value of gamma that I need to fit observations
Eugenio Bianchi: erez agmoni gamma being equal to that is very natural. From the perspective that I try to emphasize at the beginning that it is the breaking of scaling alliance which should be what one hundred
Alejandro PEREZ: controls the coupling between the granular and
Alejandro PEREZ: and and in the low energy
Eugenio Bianchi: I see. And the question is, there are many proposals that Don't go under the name of its inflation, but they are not exactly the same mechanisms, same models in lagrangians, same initial conditions.
Alejandro PEREZ: No, I don't think so,
Alejandro PEREZ: but i'm not one hundred percent sure, because I am not familiar with absolutely all the literature yet, but we haven't found anything like this. First of all, here in Hicks inflation. The heat is the engine of inflation by the Higgs rolling in exponential.
Eugenio Bianchi: Yeah, this I understand that. So the question was, If there's some
Abhay Vasant Ashtekar: from the scheme, you add in part, it is a ratio Gamma or Lambda Square the
Abhay Vasant Ashtekar: and then for the I mean the the the it's a lambda. It's not that Lambda covers it right. I mean It's a it's a combination of those two coupling costs that is, go. I mean, the way you are. It It looks like you
Alejandro PEREZ: Gamma appears here.
Abhay Vasant Ashtekar: Yeah, but this is a free parameter,
Alejandro PEREZ: and in in the he that's what I would say.
Abhay Vasant Ashtekar: Everything is meeting up. Thank you very much for the impatient. I. We use this stochastic
Alejandro PEREZ: to in this reasoning of energetics.
Alejandro PEREZ: I mean eventually what I believe is that all this come naturally from the fact that in lucrative. There are no perfectly symmetric states, and that if we are able to describe the
Alejandro PEREZ: it's
Abhay Vasant Ashtekar: Yeah, it's a very nice idea. But I don't agree with your passing remark you made that in this case there is no issue about class cont to classical transition. That is, you just put it by hand
Abhay Vasant Ashtekar: that this thing is just stochastic. There's something called of gravity, and I put it in stochastic one. So you just put it by hand to solve the problem.
Abhay Vasant Ashtekar: I agree to some extent. But what I want to say is that the vacuum in quantum field theory
Abhay Vasant Ashtekar: these are symmetric states. What i'm saying is that here. The idea is that at the heart there are no such things as symmetric states we cannot construct a symmetric state in,
Alejandro PEREZ: to begin with. Why, in the standard picture.
Alejandro PEREZ: We have the bunch, David Vacuum, which is homogeneous and isotropic.
Abhay Vasant Ashtekar: Yeah, that's that's a it's not related to your talk. So thank you.
Jorge Pullin: If the includes Tanker, the handwriting.
Thank you and the group.
Alejandro PEREZ: Thank you. Thank you.