Jorge Pullin: speaker today's return areas will speak about vacuum state for the quantum cosmology.
Rita Neves: Thank you so first of all thank you to the.
Rita Neves: organizers for giving me the opportunity to give the seminar.
Rita Neves: And that's my name is super nervous i'm a PhD students and my second year that Mr competency they muddied and my supervisors on Mrs marketing manager Javier or middle.
Rita Neves: And today i'm going to talk about the work that we are, we are finishing now and we should have submitted for publication soon, and it is on a proposal for a vacuum state of cosmological perturbations in quantum cosmology.
Rita Neves: So we started cosmological perturbations because they give us the connection between physics, of the very early universe and observations from this end.
Rita Neves: In in standard cosmology they're usually studied by imposing initial conditions at the onset of inflation, because shortly before there is the bank severity and at this point, there is a notion of preferred vacuum which is a bunch Davis vacuum.
Rita Neves: So they can be evolved and they their perspective can be concluded at the end of inflation and be compared with observations.
Rita Neves: However, English quantum cosmology and in other theories of quantum cosmology that resolve the singularity that there is, we have inflationary dynamics and so there is no longer motivation to to fix initial conditions of perturbations at the onset of inflation.
Rita Neves: And we might want to choose them to define their initial conditions at an earlier time in a quantum cosmology usually this time is chosen to be at the bounds, that we can be chosen before.
Rita Neves: But wherever it is chosen, presumably.
Rita Neves: These perturbations will reach the onset of inflation in an excited state with respect to the much Davis vacuum of standard cosmology, and this will have an effect.
Rita Neves: On on the predictions of our spectrum and so on comparison with observations, so this opens this observational window for quantum gravity.
Rita Neves: And, as I said, we have a freedom and choice of initial time for inch before cosmological perturbations where we said vacuum, but we also have a freedom in the choice of the vacuum states.
Rita Neves: And the theory doesn't have enough symmetries so as to define a unique vacuum states, and so this leads to the question of whether whether there is a notion of natural vacuum and.
Rita Neves: So in this respect, they have me many words done and the most popular prescription is set at the batek initial conditions for perturbations, it is very popular because it is.
Rita Neves: it's a very practical they're easy to compute.
Rita Neves: And, but they at the Vatican usual conditions are somewhat and satisfactory as a as a natural vacuum so other attempts have been other proposals have been constructed and for vacuum state of cosmological perturbations.
Rita Neves: For example, the diagnosis of hamiltonian the minimization of the paranormal I stress energy tensor for of uncertainty relations and also the minimization of smeared quantities and the proposal we're going to show today.
Rita Neves: is one that minimizes this new quantity.
Rita Neves: So let me start with them some context and notation so we have our our geometry, and we have a football field five.
Rita Neves: Subject to a potential, with this report, and you will receive Dr inflation and we study on it on our background.
Rita Neves: We impose killer and tensor game gauging various situations which are many will, coupled with the geometry Q amp T and T here the I you know to to possible polarization of cancer perturbations.
Rita Neves: Usually, we also do first the redefinition of our fields within a factor of the scale factor to this conformal us and.
Rita Neves: And then we expand them in for you modes and in this way, and similarly for and, obviously, for the 10th remotes were either here is comfortable time.
Rita Neves: So we then find the equations of motion of these two fields, you and you.
Rita Neves: Still, are intense remotes, and here the the prime denotes derivative with respect to conformal time eater and K case the mode.
Rita Neves: And these terms SS as the vastness of tea are the time dependent mass functions in standard cosmology these terms.
Rita Neves: Simplifying those scenarios and to minus a prime prime rate, however, independent cosmology they haven't more complicated for any particular therefore depends on the the approach that is adopted to incorporate perturbations within the framework of reporting cosmology.
Rita Neves: In this work we're going to use we're going to follow the hybrid approach so we're going to use the terms that come from the hybrid approach for this could be also adapted to other approaches such as address metric approach by simply using the the corresponding time dependent malfunctions.
Rita Neves: Attempts so the in the hybrid approach the tensor the the term for the sensor modes depends on the on background variables scale factor energy density plan for the pressure.
Rita Neves: And the one for skill or modes has an extra term which depends also on background variables and all the input on the potential of me photon and derivatives of it with respect to the to the field to fight.
Rita Neves: And, of course, with this with this form we don't have a vehicle solutions for the equations of motion, and we, we have to integrate in America we given initial conditions.
Rita Neves: Once once we do that, then we can we can evolve these perturbations.
Rita Neves: And until all the scales of interest have crossed the horizon, the during inflation and when the perturbations moving freeze.
Rita Neves: And at that moment we compute the perspective, the one for the moving moving moving curvature perturbations and and for cancer Moses work, and you can see that the spectrum is proportional to the complex known square of these of these fields.
Rita Neves: So, as I said at the Vatican so conditions are one of the most popular prescriptions to fix initial conditions for cosmological perturbations and we will end up comparing our results with an aerobatic at the Vatican usual condition, so let me very briefly and.
Rita Neves: show how these are are found, and they actually come from antibiotic states which were introduced as a an approximate solution to the equations of motion, they are built by first imposing the sunsets.
Rita Neves: and introducing it integrations emotion, or anything in the equation of motion and then finding the equation of motion for the function w here.
Rita Neves: And then add the robotic state of finite order is one that tends who's who's w function tends to this one in the limit of large case at least SK to N minus one half.
Rita Neves: Now there isn't one single procedure to obtain another state of Oregon order and the one we're going to use here we have obtained by finding the state of water inputs to find searching on the right hand side of this equation is the one order n.
Rita Neves: And, and obviously here in the western will have used either this killer time dependent mass or to cancer time depending.
Rita Neves: on which one we're analyzing and we need to start with a zero Florida being just OK.
Rita Neves: Now the stage we're going to propose as vacuum states for the perturbations are the so called states have low energy, you have been defined in this paper by oberman.
Rita Neves: and
Rita Neves: That work is actually based on a result by fewster early result which shows that the normalized energy density smeared along the timeline curve, with a point depleting procedure is bounded from below, as a function of the state.
Rita Neves: So then oberman particular as this result for cosmology for generic models using smearing function that is supported on the world line of the nicer Tropic observer.
Rita Neves: And in the same paper he defines a procedure to find the state that minimizes this quantity this meaning the smearing it, this means energy density by minimizing it all by mode.
Rita Neves: And we believe these are viable candidates for vacuum of motivations in cosmology because, firstly because minimize the risk of life energy density and also because they are proven to be exactly how much states.
Rita Neves: And this is an advantage, because this guarantees that certain computation switches that of distress energy density will be well defined.
Rita Neves: it's also an advantage because constructing explicit harlemites States as far as we know, is a very difficult task, or even just proving that state is proving explicitly state is hello, Mr this gospel.
Rita Neves: A very non trivial, and so we have a procedure that gives us states that you know will have this mathematical properties.
Abhay Vasant Ashtekar: do have a.
Abhay Vasant Ashtekar: Quick explanation about perhaps what the relation of disease, with the work of the Nelson Nelson and I had done in which we are also found very normal as as a tensor and found a unique state, but that require that you instead of time, this does not require any stretch of time.
Rita Neves: No, this is not require any say I will explain that will be the procedure, so I think that will be more clear.
Abhay Vasant Ashtekar: Thank you.
Rita Neves: So let me start by just giving the notation that open uses, we are, this is for a generic.
Rita Neves: model and the generic field T, which has this equation of motion, and here the dots is derivative with respect to cosmological time.
Rita Neves: He is the fact, so if you're using we're analyzing skill or a tensor perturbations misty would be our view or team, and we have would have to.
Rita Neves: Use the correct Omega here, which is given in this way with respect to the form, I showed before of the questions of motion, but we just have here the time dependent mass term which would be either for scale or tensor perturbations now written in terms of the cosmological time.
Rita Neves: And so what we want to find the state that minimizes the most contribution to the smeared energy density.
Rita Neves: So we have the the energy density here pie, is the conjugate momentum of tea, we can read it in terms of velocity as oberman shows.
Rita Neves: As oberman does.
Rita Neves: And it is smeared with this missing function along the defined my curve.
Rita Neves: So the total energy density will be.
Rita Neves: A Sam over all the all of the modes, and this is more contribution.
Rita Neves: So now here this meeting function shows up squared.
Rita Neves: And this is a detail of sisters results, and we will define directly a squared.
Rita Neves: F chord this has to be a test.
Abhay Vasant Ashtekar: function, so it has to be a.
Rita Neves: Positive competitive support and support so we'll define will we will call usually the test function directly if script and the procedure is as follows, we start with an arbitrary solution.
Rita Neves: As opposed.
Rita Neves: To the question of motion and we find a city, we perform a billy Bob transformation here Lambda new are the bully of aqua efficient they're usually called one time data.
Rita Neves: And so they are complex variables, we have four degrees of freedom to complex Norman complex face of each minus one even from this.
Rita Neves: relation will write the complex normal blunder with respect to that of view.
Rita Neves: We will also fix new to be positive, a positive real value, because we can be find TEE up to face.
Rita Neves: We defined here to face, and so we just have the now two degrees of freedom, new and the complex face of London.
Rita Neves: And, before moving on will also defined these two quantities you want and see to.
Rita Neves: Which are fixed for a given solution so unforgiven mode and.
Rita Neves: See one is, essentially, it is the ear of so the mode contribution to this weird energy density of this s.
Rita Neves: solution.
Rita Neves: It is always positive, and it is always greater than the complex norm of see to.
Rita Neves: also note that this quantity once you want it to carry a dependence on the test function F.
Rita Neves: So we can write the quantity want, we want to minimize eft we can read it in terms of new and the complex phase of Lambda.
Rita Neves: I did, right here the complex number of lump that this is fixed on you.
Rita Neves: And we see that the first term here is is always positive, because new is real and see what is positive and so minimizing.
Rita Neves: He means that we have to fix the face of lumber such such that discuss it minus one now we just have the in terms of written in terms of new and this is a standard minimization problem.
Rita Neves: We minimize he with respect to new and new a new.
Rita Neves: And then we also obtained rather.
Rita Neves: than the face was already fixed and the complex norm is obtained by me and notice here that everything is well defined because this quantity is always is always positive.
Rita Neves: And so, this defines the state of low energy associated to the smearing function.
Rita Neves: F is fine, through the volleyball transformation, where now the coefficients mom you are defined the way we did just now.
Rita Neves: and note that it is associated to this main function, because we do have dependence on the smearing function, it is ins, you want to see to.
Rita Neves: Obama also defines a state of minimal energy.
Rita Neves: As a state that is of low energy for any as any test function, however, immediately proves that this this state only exists in otter static space time zone will be will be a very useful for our case, and so we will have to deal with the dependence on the smearing function.
Rita Neves: And this this questions the.
Rita Neves: universality of the proposal, if we are, we are trying to propose a unique vacuum, you need natural vacuum and we are introducing an ambiguity in the choice of test function.
Rita Neves: And so we wonder what is the relation between this the the state of low energy and the natural vacuum in or natural vacuum in in maximum asymmetric space times, so I mean cascade is trivial trivial see.
Rita Neves: that the state of Hawaii energy is indeed the identical to.
Rita Neves: cascade vacuum and the way to see that is just by starting with and there's the initial solution being the wrinkles vacuum and we find that cities identically zero, and so this means that Lambda.
Rita Neves: Lambda is one up to face new is zero.
Rita Neves: And the volleyball transformation, then gives us that this the state of where energy is mikulski vacuum, up to a face.
Rita Neves: In the sitter, the situation is not trivial it's a bit more involved, and you can also find that the procedure does single out the bunch Davis vacuum when the support of F is in the distant past.
Rita Neves: This has been proven for the case of the massive field and in the work we should be publishing soon we're going to also include proof that this is the case of the muscles.
Rita Neves: For the muscles field, so we do need the support of after be in the distant past, and then we recover the preferred vacuum.
Rita Neves: There are some.
Rita Neves: properties that are of interest for us in this for this states, these are all studied in this paper, which is very thorough and has now also other interesting properties and the first one is that have been depends on this edition of solution so obviously this had to be the case.
Rita Neves: Where we have basically minimization problem, so we can the solution, the result cannot depend on the financial solution for in this paper they have.
Rita Neves: proven explicitly that that is the case, and they have also device actually a strategy to obtain a different procedure to obtain the state of Hawaii energy without requiring a a financial solution.
Rita Neves: And, but since this procedure doesn't have any particular numerical advantage we're still going to use the one I just described by Alderman.
Rita Neves: You also find that the state of the energy admits.
Rita Neves: ultraviolet and infrared expansions so that means that there is at least an analytical control of the sympathetic behaviors in the ultra violet find that the complex norm.
Rita Neves: which is what we need for our spectrum is independent, on the test function and that thing certain behaviors also mean cost you like for all test functions so essentially the ambiguity of test function will be in intermediates it will affect intermediate scales.
Rita Neves: Finally, given these.
Rita Neves: These analysts analytical control of the psychotic behaviors they also find that when they use a vacuum states are for perturbations there is an agreement observations.
Rita Neves: And in cosmological model models that have a period of kinetic dominance prior to inflation so basically they did they find that the behavior of the Prospector has the qualitatively has the validity correctly, the behavior to agree with observations.
Abhay Vasant Ashtekar: But that is only if you choose the the test smearing functions to be peaked at those times right.
Rita Neves: Well, no, that is where we're going to show they show this this conclusion is independent of the test function because.
Rita Neves: They have shown before that the behavior doesn't protect behaviors are independent of this function.
Abhay Vasant Ashtekar: Right, but that, but there will be.
Abhay Vasant Ashtekar: Some topic, be able to locate but I know you can have a disagreement with the observed spectrum as eloquent hundred.
Abhay Vasant Ashtekar: Yes, if you choose such states and so therefore I think when you say agreement is observations of cosmological models with kinetic dominance, but I to inflation, unless it is fine tune this meeting function is fine tuned to this.
Abhay Vasant Ashtekar: minute.
Abhay Vasant Ashtekar: You.
Abhay Vasant Ashtekar: get agreement with cosmological.
observations.
Rita Neves: Yes, so what I mean by this Maybe I should have clarified this is, this is only the agreement interesting topics, so we still have an open question of whether there is a necessity necessity for fine tuning of the best option for intermediate skills to agree as well with observations.
Abhay Vasant Ashtekar: Right, but what will actually observe these intermediate scales.
Abhay Vasant Ashtekar: Right, what does not opposite K going to infinity.
Abhay Vasant Ashtekar: Or what when observes only certain from you know 10 times the traditional scale that was used by.
Abhay Vasant Ashtekar: By w map to about 2005 and 2000 times that's scale so it's really intermediate scale So what does not absorb infrared or ultraviolet.
Abhay Vasant Ashtekar: Also, have nothing to say, we can pray God alcoholic.
Abhay Vasant Ashtekar: So it's nice mathematical, but I think once you sort of draw a distinction between this perturbations I mean between the mathematical results and agreement of observations.
Rita Neves: I me.
Abhay Vasant Ashtekar: And there's other thing was that well if you just use this test functions to be very sharply peaked at you will instruct of time, the States that are obtained year must be very close to the states that.
Abhay Vasant Ashtekar: argue and Nelson and I were talking about writing.
Abhay Vasant Ashtekar: Because we are that we are their muscles, so these days have an infinite number of inflated dimensional freedom because that's functions is in three dimensional space.
Abhay Vasant Ashtekar: Whereas the ones that were were were come down that freedom to just one parameter, which has to do with it with the history of time, this is just for general information, this has nothing to do with your time, thank you.
Rita Neves: Yes, what we're going to show is actually that.
Rita Neves: This ambiguity is much less.
Rita Neves: Serious or effects much observations, much less than one might show, at least in the context that we have investigate this is what i'm going to show, so we can maybe discuss this a little bit further ahead.
Rita Neves: Right so.
Rita Neves: All of these seem to indicate that these are at least.
Rita Neves: good candidates for vacuum of logical progression plus in the quantum cosmology we do have a period of kinetic dominance price inflation and so we're going to study the States and in the quantum cosmology.
Rita Neves: Okay, so to do that, we first need to obtain an as an initial solution to the question of motion numerically, of course, we need to give initial conditions, but I recall that these are irrelevant.
Rita Neves: And because as itself is irrelevant choice of rest, so he gives us zero order antibiotic initial conditions at the bounce just because they are not simple, and we also need for concreteness, we need to choose a particular.
Rita Neves: Potential for the inflict on which is a quadratic one for simplicity.
Rita Neves: The which you which you say that the procedure to find the state of our energy will not be additionally complicated with different potential for this killer fields.
Rita Neves: And for this potential we fix the mass of the scholar field to be this value this is constrained observations through content cosmology.
Rita Neves: And we also need to choose to fix the perimeter of the background.
Rita Neves: Which is the value of the inflict on at the bounce.
Rita Neves: This value, we have chosen looks very specific, but it does require some tuning.
Rita Neves: And in the same time, when to explain now, so this.
Rita Neves: i'm showing here a plot, this is from plonk 2018 results, the report a forum for results on inflation and it's showing and.
Rita Neves: Essentially, the the possibilities for the power spectrum.
Rita Neves: So the regions where the specter of the commuting curvature perturbation it can can be for way can also.
Rita Neves: And as you can see, there is a region here that is very, very.
Rita Neves: flat very.
Rita Neves: narrow and so in this region, we do not want to have oscillations and in this region, they can they can occur, and we can still have an agreement with observations.
Rita Neves: And the value of the foot on at the bounce will affect this in the sense that, if we choose a very small value for the for the foot on the bounce.
Rita Neves: We will have to literally fault, and we will end up with a power spectrum in the week with oscillations in the region, we don't we do that is forbidden by observations.
Rita Neves: And by the way, this is just an illustrative bought, this is not an actual construction of about spectrum if we choose very a lot of value that is too large, then we will probably agree with observations, but then we want to part in any way.
Rita Neves: From standard cosmology predictions, and so we have chosen value that at least gives the chance of agreement observations in the sense that we will only have affiliations, in the region where they can exist.
Rita Neves: But also the parts of it from predictions from Center cosmology.
Rita Neves: And so that is why we have chosen this value, but there is a range of values around it, for, where this collective behavior will also happen, and in that sense, it is a toy from the range of it has been tuned but the actual values as a 12 value.
Rita Neves: Once we have the the initial solution, then we need to choose the the destruction, this is the crucial part of the week.
Rita Neves: So, usually know quantum cosmology not referring to set the stage for energy now there are two strategies for choosing initial conditions for perturbations we do.
Rita Neves: Usually fixed them at the bounce or at the last topic time or before the balance and the balance is natural natural moment because it's where.
Rita Neves: quantum description of geometry is most important, but nothing, nothing is forcing us to do to fix it fix them at the bombs, we can to to the message of the time or before the bounce this has also been explored in previous works and So here we also find two.
Rita Neves: main strategies and we don't need to the financial conditions now per se and but we didn't have to choose the test function, this is the ambiguity.
Rita Neves: So you can either choose choose it to to have support on the whole evolution, by which I just mean a wide enough window in the evolution around the bounce because it is completely supported.
Rita Neves: And, and the idea here is that the observer, that is, measuring this energy density, it can be allowed to witness the whole evolution, because we have the dynamics, we have pre bouncing dynamics as well.
Rita Neves: And in this result we actually find that the state of energy that we obtained from it is very insensitive to the shape.
Rita Neves: Of dysfunction and also to its support, as long as it is wide enough if we start with a test function, that is, Peter on the bounce and restart increasing its support, then we will find that it converges very soon.
Rita Neves: However, one might also say that this is an eye view because.
Rita Neves: The situation in the quantum cosmology is is pretty simple fight with respect to the full year respect to quantum gravity and which is probably why we obtain a.
Rita Neves: An isometric bounce and so prebon dynamics might be completely different coming home for theory and if we want to remain agnostic about this, then we can we can choose F to be X squared to be supported only on the expanding branch so starting at the bounce and onto the future.
Rita Neves: And in this case.
Rita Neves: We will choose an APP that is sharp step function, so that it is, it does include the bounce we don't want to erase the balance completely.
Rita Neves: But it is smooth and I will show me exactly the form is if we have used in a minute.
Rita Neves: And this in this scenario, we also find that results are insensitive to the support, as long as it is wide enough.
Rita Neves: We have we are going i'm going to show results for an F that starts at the bounce and ends at the onset of inflation, but we did we did test check that we end the support sooner or willing to inflation, the state of Hawaii energy will be exactly the same.
Rita Neves: So these are the two strategies we're going to explore.
Rita Neves: The one for you have supported on the whole evolution and the one to put it on the expanding brand show me and, as I said, we're going to use a smooth set function.
Rita Neves: we're going to build build it with this auxiliary function, which is just it gives us the ramping up from zero to one in a smooth way, and so we define if in in branches, we have we have ramping up constant value when they ramping down.
Rita Neves: And we parameters it with.
Rita Neves: With delta delta is the time between the time the function takes to go from zero to one and from one to zero so for the whole evolution.
Rita Neves: For the case where F is supported on a wide enough period around the bounce.
Rita Neves: The value of the delta is irrelevant, it makes no difference for the expanding branch.
Rita Neves: whenever you supported on expanding branch, we do not want to dampen the the contributions coming from the bounce we are going to start that the bounce so either I will be the bolts therefore we're going to use the delta that is very, very small.
Rita Neves: So that this goes to one here quickly.
Rita Neves: So now we have everything.
Rita Neves: defined, and we can compute.
Rita Neves: The the sea one Institute, which gives us the volleyball coefficients and finally compute the state of low energy.
Rita Neves: And so Now let me show some some results first thing i'm going to show the initial conditions we obtained from the state of energy, by which I mean.
Rita Neves: The value of the state of energy and its confidence velocity and at the bumps so we have an official solution as okay along the whole evolution well or along the window, the period where we that we are interested in.
Rita Neves: And we obtain a state of energy also for for this whole time but so that before so that we have something that we're familiar with to compare we're going to.
Rita Neves: Do i'm going to show the initial conditions parameters in this way, this is the usual way to monetize them now, a parameter has a configuration with a positive function D and the velocity with the and also a any real controversy that is any real function.
Rita Neves: And these are the results we obtained for.
Rita Neves: scaling mode, this is for scale of months.
Rita Neves: So if you.
Rita Neves: If you look at the or were saying before, is that the autopilot behavior is independent of this we can verify here and infrared behavior is mycoskie like for both.
Rita Neves: though they different by a constant factor here, of course, which is dependent on this test function.
Rita Neves: and
Rita Neves: However, if we look at see then we do get a different entirely different kinds of behavior between the two possibilities for the test function.
Rita Neves: Even though the scale is very small, so the actual difference between the two is very small.
Rita Neves: Now this is the result for scale or modes and we get exactly the same thing for cancer modes module some differences.
Abhay Vasant Ashtekar: What is zero is that the bernstein.
Rita Neves: Yes, there is the pants yes.
Rita Neves: And so, for scaling decimals you get essentially the same thing.
Rita Neves: And this.
Abhay Vasant Ashtekar: might seem surprising at first.
Rita Neves: But it's actually easy to see that this had to be the.
Rita Neves: case because at the bounce the.
Rita Neves: Time dependent masters of.
Abhay Vasant Ashtekar: skin cancer most are very close because of.
Rita Neves: The term that is different.
Abhay Vasant Ashtekar: between them.
Abhay Vasant Ashtekar: is essentially zero because we.
Rita Neves: Have a kinetic.
Abhay Vasant Ashtekar: dominated bonds.
Rita Neves: And as valid.
Rita Neves: As itself is relevant, so we can choose any initial conditions we want for it and we have chosen.
Rita Neves: 01 at the bottom ones, which are the same force killer and presenter mode so essentially we are starting with a solution that at the bounces same preschooler intensive modes and we have an equation of motion that at a period around the bounce.
Rita Neves: is very similar so of course this will maintain the similarity between the two around the box.
Abhay Vasant Ashtekar: i'm confused about what is F of what is the spirit function here.
Rita Neves: that's my function is in red, we have the one that is supported right enough period around the bounce it's a window function.
Abhay Vasant Ashtekar: So Hollywood Asian doesn't mean the whole.
evolution.
Rita Neves: quotation marks yes.
Abhay Vasant Ashtekar: Okay, no that's fine, so how big is that.
Rita Neves: yeah we this was computed at around 64 seconds around the bounce we have seen that it can.
Abhay Vasant Ashtekar: Make sure what size 60 seconds.
Rita Neves: 64 in total.
Abhay Vasant Ashtekar: Total okay.
Rita Neves: we're good to.
Abhay Vasant Ashtekar: Go to Egypt and expanding graduate, which is supposed to be what.
Rita Neves: Expanding branches a window function, starting at the balance and, in this case it's ending at the onset of inclusion.
Abhay Vasant Ashtekar: Thank you.
Rita Neves: Okay, so it is easy to see that we are getting the same thing we should have seen the same result for initial conditions at the bounce obviously then still intensive modes will behave differently throughout the occlusion away from the bumps.
Rita Neves: So now where we're going to compute power sector for moving curvature perturbations and denser mode as well.
Rita Neves: At the end of inflation, or rather, when all the scales of interest have crossed the horizon.
Rita Neves: And i'm showing here in the top panel, the one for skill or in bottom Panel for tensor molds for the same two types of tests functions, the whole evolution supported on.
Rita Neves: Whole evolution and expanding branch and, as you can see, they are essentially I mean they effectively they're the same color spectrum.
Rita Neves: Even if I zoom in, we can see that there are numerical differences.
Rita Neves: But at least qualitative we were thinking exactly the same result even quantitative easing essentially saying the same thing, so it seems that.
Rita Neves: Even though we do obtain differences initial conditions and the least the predictions of our spectra.
Rita Neves: are very insensitive to the choice of test function which.
Rita Neves: is too much.
Abhay Vasant Ashtekar: I said I don't think is very insensitive because I think that what is observable spectrum would be about I didn't attend to them a few times 10 to the minus five.
Abhay Vasant Ashtekar: To about 10 to the minus to adjust your manager and so, as you can see that there are all these oscillations, whereas the badge Davis Prospector tool that will not have any a bad it just.
Rita Neves: With respect to the bunch this one is different i'm i'm just comparing two different types of functions.
Right.
Abhay Vasant Ashtekar: So Okay, so what is.
Abhay Vasant Ashtekar: Like okay so you're saying that with respect to the changing the test functions you don't get very much, yes, but in terms of actual observations, yes, good would be that would be differences.
Rita Neves: So here, I was just pointing out that this ambiguity that we have that was kind of.
Rita Neves: The biggest obstacle and considering this a possible definition of a natural vacuum effectively disappears this list, of course, within the scenarios and.
Rita Neves: Also, we find that this interestingly, this is essentially the perspective one of things.
Rita Neves: perspective one up thanks for second order antibiotic initial conditions at the boss, so this is second order notice it's not 00 for the motto, and we have used for the traditional solution and.
Rita Neves: don't observational they're very close, we should stress that that they are fundamentally different as as vacuum States and because that's why energy obviously obviously minimize this mood energy density.
Rita Neves: And they are exact how much states, so this means that we can safely.
Rita Neves: Do competitions of those jets energy sensitive potential and an antibiotic states of second order does not allow us to do that.
Rita Neves: So.
Rita Neves: It is interesting to note, though, that if we want to approximate the state of Hawaii energy, then we can do so with a simple State that is the second already voted one.
Rita Neves: But then, if you actually want to do further competitions from it, we should use the state of Hawaii energy.
Rita Neves: We have also completed the temperature sensor to scale, the ratio, so the ratio between tensor power spectrum and scale of our spectrum.
Rita Neves: and
Rita Neves: And here we just wanted to point out that we do get near scale environments mature, we are done in the power spectrum, this is this is in line with.
Rita Neves: Previous findings of other proposals for welcome states.
Rita Neves: And again, we get.
Rita Neves: The same predictions for the two types of functions know we also wanted to get an idea so so.
Abhay Vasant Ashtekar: Are you writing this plot talking about this one in the previous are very primordial pride spectrum or, this is the the primordial pops up spectrum is what you're proposing.
Abhay Vasant Ashtekar: At the end of inflation right yeah so.
Abhay Vasant Ashtekar: By model we're not the observer Okay, thank you.
Rita Neves: So we also wanted to get an idea of where of where these results line, the whole realm of.
Rita Neves: of observations and.
Rita Neves: Though we did not.
Rita Neves: We were not intending to do a rigorous logistical analysis, yet, would you compute the tensor to scale ratio at a given a particular scale.
Rita Neves: And this is so we can prepare with observations and the spectral index, which is related to the slope of.
Rita Neves: Our spectrum of skill perturbations that's where where when near it's killing variances rich.
Rita Neves: And i'm showing here plot, this is a local plot plot also by the plan collaboration of the 2018 results on inflation.
Rita Neves: That shows in these blue red and green regions, the.
Rita Neves: The allowed the regions for confidence levels of 68% and 95% for four different data banks, so we can compare with.
Rita Neves: Each and it also shows predictions for popular models of inflation and LUCAS visionary models in this in these lines, and in these regions in in purple yellow and green.
Abhay Vasant Ashtekar: So, which which one is a five squared that you're using I can't see the color.
Rita Neves: Is this one.
Rita Neves: You can see very well and the five squared is this one this yellow on the line between the two, the two circles, not the whole region, just this line here, and these two circles correspond to 50 equals and 64 bits of information yeah.
Rita Neves: So our results will lie more or less of that this point and and firstly, we should note that, first, one might say that this is not a great.
Rita Neves: Agreement with observations, at least for the tensor discoloration the primary field is perfectly within mean values and an error bars given by the plank collaboration and that, but the tenses the discoloration with high, however.
Rita Neves: We did use the quadratic potential for the scale of fields, so we actually should be comparing more with this line, and so we do see that.
Rita Neves: As I said, this goes from 50 equals inflation to 60 and value would have chosen for the scale of feel that the bounce actually is getting 77 I think a filter inflation so it's a bit further ahead.
Rita Neves: So what we want to point out from here is that even with just this toy value for background variables and.
Rita Neves: These states have low energy at least give us as good an agreement of the observations just from this very rough analysis of course.
Rita Neves: As standard cosmology.
Rita Neves: And so.
Rita Neves: Let me summarize by saying, first, that we pointed out, the state of war energy in journal have the capacity of being good candidates for regular because there are part of our state's you minimize the mood energy density and at least us in politics are.
Rita Neves: under control and are independent of the test function.
Rita Neves: Also, have seen that there is.
Rita Neves: And in this previous work that there is an infrared and ultraviolet agreement globally, rich in models where kinetic comments proceed efficient so, at least within these models.
Rita Neves: These seem to be good candidates for vacuum now in new content cosmology we saw that we obtained at least that qualitative agreement observation as much as standard cosmology but, more importantly, we think we have proven that.
Rita Neves: The results are pretty insensitive to the choice of test function, so this proposal.
Rita Neves: had one major let's say this advantage which was that introduced an ambiguity in the choice test function, but we do find that are in at least within these.
Rita Neves: Natural choices and weaving hybrid look one of those modules, although this would probably happen as well for other frameworks and.
Rita Neves: This is ambiguity effect when he disappears when we look at the results.
Rita Neves: So we we do believe that this would require more rigorous statistical analysis and that will mean.
Rita Neves: not only of the parameters of the background, but also applying this procedure to different different framework or two different prescription, such as the dress metric approach and comparing the two.
Rita Neves: And then, if we do want to do a reverse statistical analysis and compare with observations properly, then we would also have a would also be ready to choose a potential for the input on that is more favorite by observations, because we can actually say something about the theory.
Rita Neves: So thank you, this is all I wanted to say thank you for your attention, and if you have questions i'll be happy to answer.
Jorge Pullin: questions.
Abhay Vasant Ashtekar: So let me just ask.
Abhay Vasant Ashtekar: A couple of questions, but the first is really not, I think I know the answer, but I don't think most people understood the I shouldn't say that not a people may not have understood the The important point you emphasize couple of times that the choice of these bases SK doesn't matter.
Abhay Vasant Ashtekar: So this, therefore, the initial conditions you're putting here also don't matter so, can you just explain, for everybody once again why that is a case.
Rita Neves: Well, that is the case because.
Abhay Vasant Ashtekar: Go back to the slide that yeah.
Rita Neves: Well, this one is the case because, and one way to pay well this first of all, this is a this minimization problem, we need a concrete solution to start the procedure but.
Rita Neves: It is easy to understand that it shouldn't depend on in this initial solution, so what happens is that when we we define a nsf K, we are obtaining a certain pair of.
Rita Neves: volleyball coefficients that minimizes is quantity if we choose another K, we will still obtain the state that minimize that quantity and what will happen is that the volume of coefficients will be different ones, they are dependent on this solution.
Rita Neves: But they will still minimize the the quantity, where we want, so the smeared energy density.
Abhay Vasant Ashtekar: Different choices of.
Abhay Vasant Ashtekar: Basically, is like.
Abhay Vasant Ashtekar: Well, I think there's a very non trivial point because different choice of escape give you can give you.
Abhay Vasant Ashtekar: Really different representations, they can be literally equivalent if you choose this different ones, but I think what the what you're saying is that, but the representational you're choosing by minimizing the energy is.
Abhay Vasant Ashtekar: So to say.
Abhay Vasant Ashtekar: Is a well defined representation or it's a well defined complex structure by that minimizing energy requirement.
Abhay Vasant Ashtekar: For a given dresser fk.
Abhay Vasant Ashtekar: And then the statement is that that complex that she could be obtained, I mean it just exists, and this is just a way of obtaining that.
Rita Neves: Yes, this.
Rita Neves: is just an intermediate state exists, that is the result by sister.
Rita Neves: Is that this this exists.
Rita Neves: yeah well Alderman is, it is a procedure to to find this one.
Abhay Vasant Ashtekar: And the other thing is that I just feel that you know it's very, very beautiful work is very nice, but I think what you're done is really chosen.
Abhay Vasant Ashtekar: To test functions right, yes, which would you motivate in some way, but I think to conclude from there that the whole thing is robust and doesn't depend on the choice of test function is red is too strong, I think that you might just say that, well, I think that there's a class of.
Rita Neves: These even these choices, but the question is that we did to within these two choices we also studied, particularly in this one whole evolution, we did choose different shapes for the test functionally choose different supports will test function.
Rita Neves: And we did find that they were converting to a to one state now if we're just looking at the second one, then also there would be other possibly nice natural more fine tuned choices of this test function which indeed would give different.
Rita Neves: results, but we are trying to find natural choices and then maybe in the future, we can explore.
Abhay Vasant Ashtekar: Well, I think this is very nice but it's just that function as is very complicated right, so what one might say, think of as being you know.
Abhay Vasant Ashtekar: Natural choice may sometimes be just a set of measures zero in the space space of functions.
Abhay Vasant Ashtekar: So, so therefore I think, to say that this doesn't really depend on the test functions, is, I find that is a very strong statement.
Abhay Vasant Ashtekar: But.
Rita Neves: Even these these choices, of course.
Abhay Vasant Ashtekar: yeah exactly so we did the class of.
Abhay Vasant Ashtekar: choices that you're considered to be.
Natural.
Abhay Vasant Ashtekar: yeah Thank you.
Abhay Vasant Ashtekar: Thank you.
Jorge Pullin: questions.
Jorge Pullin: Okay, there are no other questions, so thank the speaker again.