0 00:00:02,210 --> 00:00:08,379 Jorge Pullin: Okay. So our speaker today is Alexandra Pitts will speak about inflationary phenomenology from plank and discreteness. 1 00:00:09,310 --> 00:00:20,790 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 2 00:00:20,800 --> 00:00:23,889 Alejandro PEREZ: for for maintaining this seminar over 3 00:00:30,380 --> 00:00:38,190 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, 4 00:00:38,800 --> 00:00:43,110 Alejandro PEREZ: and it has to do with the 5 00:00:43,420 --> 00:00:59,769 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. 6 00:01:00,710 --> 00:01:07,789 Alejandro PEREZ: So I am using my tablet, and so I should be able to write on top of the slides 7 00:01:08,710 --> 00:01:14,340 Alejandro PEREZ: uh, so which will allow me to, you know, interact with you more easily, I hope. 8 00:01:14,480 --> 00:01:16,879 Alejandro PEREZ: All right. So 9 00:01:31,810 --> 00:01:37,869 Alejandro PEREZ: general relativity is, the classical theory is expected to arise. But 10 00:01:37,910 --> 00:01:40,309 Alejandro PEREZ: in the continuum 11 00:01:40,570 --> 00:01:49,070 Alejandro PEREZ: as an effective effective description of something of some reality that is actually discrete at the fundamental level. 12 00:01:49,080 --> 00:02:03,609 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. 13 00:02:03,620 --> 00:02:22,660 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 14 00:02:22,670 --> 00:02:40,730 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, 15 00:02:40,890 --> 00:02:44,919 Alejandro PEREZ: such as diffusion round in motion, et cetera. 16 00:02:45,140 --> 00:02:59,400 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. 17 00:03:08,220 --> 00:03:20,770 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. 18 00:04:18,399 --> 00:04:27,730 Jorge Pullin: Yes, all right. So the problem of vacuum contributions to dark energy is the problem of quantum gravity. 19 00:04:27,920 --> 00:04:47,849 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, 20 00:04:47,860 --> 00:05:01,619 Alejandro PEREZ: even though it's not going to be the central team of this talk I want to talk about, 21 00:05:08,940 --> 00:05:23,540 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, 22 00:05:25,060 --> 00:05:26,510 Alejandro PEREZ: and that 23 00:05:28,350 --> 00:05:43,329 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, 24 00:05:43,720 --> 00:05:53,679 Alejandro PEREZ: so the cosmological constant is to be provided as one more initial data, for 25 00:05:53,900 --> 00:05:55,590 Alejandro PEREZ: it is not a fundamental function. 26 00:05:55,600 --> 00:06:04,609 Alejandro PEREZ: In addition, the energy, the vacuum contribution to the energy momentum tensor does not contribute to the field equations, because it's 27 00:06:04,620 --> 00:06:17,200 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. 28 00:06:24,270 --> 00:06:31,720 Alejandro PEREZ: I believe that the problem remains in the sense that one has to provide this initial data for the cosmological, constant. 29 00:06:31,730 --> 00:06:37,709 Alejandro PEREZ: And if we think of a cosmological model where the universe starts at the Big Bang, 30 00:06:37,720 --> 00:06:57,189 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 31 00:07:06,340 --> 00:07:24,069 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, 32 00:07:24,080 --> 00:07:42,390 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 33 00:08:01,810 --> 00:08:08,310 Alejandro PEREZ: not supposed to fluctuate that is provided from it's A. It's a background volume, strategy 34 00:08:09,280 --> 00:08:16,609 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: 35 00:08:16,620 --> 00:08:30,629 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, 36 00:08:47,070 --> 00:08:55,490 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 37 00:08:55,500 --> 00:09:08,539 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, 38 00:09:09,670 --> 00:09:11,580 Alejandro PEREZ: the one as the one for 39 00:09:12,210 --> 00:09:32,050 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 40 00:09:32,060 --> 00:09:34,339 Alejandro PEREZ: and scale transformations. 41 00:09:34,350 --> 00:09:46,379 Alejandro PEREZ: And so It is this breaking of scaling variance of this um of the of the underlying volume structure which 42 00:09:46,490 --> 00:09:50,630 Alejandro PEREZ: structure of any one, and if we think that 43 00:09:50,640 --> 00:10:08,869 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 44 00:10:19,800 --> 00:10:29,930 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. 45 00:10:39,850 --> 00:10:54,600 Alejandro PEREZ: In fact, this is the effective description that arises from the thermodynamical argument of Jacobson, and it is also the 46 00:10:55,310 --> 00:11:13,420 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 47 00:11:14,660 --> 00:11:33,290 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 48 00:11:43,670 --> 00:12:02,430 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. 49 00:12:03,090 --> 00:12:16,920 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 50 00:12:16,930 --> 00:12:23,310 Alejandro PEREZ: the dark energy sector unimole. A gravity is equivalent to generative. 51 00:12:44,220 --> 00:12:59,589 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. 52 00:12:59,600 --> 00:13:00,700 Alejandro PEREZ: That's all. 53 00:13:17,570 --> 00:13:24,809 Alejandro PEREZ: Okay, So the question we are asking, Can we produce phenomenology from the tank and the sweetness 54 00:13:24,880 --> 00:13:47,099 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. 55 00:13:47,130 --> 00:14:04,800 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. 56 00:14:30,860 --> 00:14:47,760 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. 57 00:14:47,770 --> 00:15:06,889 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 58 00:15:25,400 --> 00:15:30,590 Alejandro PEREZ: you obtain this effective formulation of the gravitational theory, 59 00:15:36,480 --> 00:16:05,270 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 60 00:16:05,280 --> 00:16:08,420 Alejandro PEREZ: in which, because magical, Constant goes down. 61 00:16:09,340 --> 00:16:10,870 Abhay Vasant Ashtekar: What is L. 62 00:16:11,390 --> 00:16:28,339 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. 63 00:16:28,350 --> 00:16:31,450 Alejandro PEREZ: So it's the path along which we are integrating. The one form 64 00:17:26,300 --> 00:17:43,519 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 65 00:17:43,530 --> 00:17:50,920 Alejandro PEREZ: over the years is that we cannot really think of this, as some, you know, 66 00:17:50,930 --> 00:18:05,450 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 67 00:18:05,460 --> 00:18:21,429 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, 68 00:18:36,240 --> 00:18:49,109 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, 69 00:19:26,690 --> 00:19:30,049 Alejandro PEREZ: but only in situations where curvature is important, 70 00:19:30,060 --> 00:19:49,480 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, 71 00:19:49,490 --> 00:19:51,490 Alejandro PEREZ: and so one could actually have 72 00:19:51,500 --> 00:19:55,310 Alejandro PEREZ: known as violating effects which are 73 00:19:55,320 --> 00:20:14,249 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 74 00:20:16,690 --> 00:20:38,110 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. 75 00:20:52,260 --> 00:21:21,580 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 76 00:21:21,590 --> 00:21:26,350 Alejandro PEREZ: and and space-time geometry with clocks and robots 77 00:21:26,490 --> 00:21:44,189 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. 78 00:22:04,710 --> 00:22:16,290 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 79 00:22:16,300 --> 00:22:31,809 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! 80 00:22:31,820 --> 00:22:58,779 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. 81 00:22:58,790 --> 00:23:01,120 Alejandro PEREZ: With respect to the excitations, 82 00:23:01,130 --> 00:23:02,560 Lee: questions 83 00:23:02,570 --> 00:23:03,520 it's 84 00:23:03,580 --> 00:23:05,200 Lee: yes uh 85 00:23:05,210 --> 00:23:23,060 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. 86 00:23:28,460 --> 00:23:38,569 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 87 00:23:39,380 --> 00:23:43,700 Alejandro PEREZ: prefer frame at the plank scale, Then this argument, 88 00:23:58,300 --> 00:24:04,940 Lee: and then I we will find, you know we will find in our experiments at Cern 89 00:24:05,100 --> 00:24:13,459 Alejandro PEREZ: that they depend on this preferred frame, and and that's what we don't actually find. Of course, in large fields. 90 00:24:26,510 --> 00:24:29,389 Lee: It's it's a start of a conversation. 91 00:24:38,320 --> 00:24:48,479 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. 92 00:24:58,260 --> 00:25:05,790 Alejandro PEREZ: And so, because the dark energy component actually grows. I will call this endothermic case because the 93 00:25:12,260 --> 00:25:16,490 Alejandro PEREZ: and I don't want to go into much much details. I just want to mention that 94 00:25:16,500 --> 00:25:17,390 Alejandro PEREZ: Bye, 95 00:25:17,400 --> 00:25:32,989 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 96 00:25:42,070 --> 00:25:52,749 Alejandro PEREZ: where one shows that actually, when one has that actually only the least of those breaking steel lines are actually, 97 00:26:08,400 --> 00:26:19,750 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 98 00:26:19,880 --> 00:26:30,950 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, 99 00:26:30,960 --> 00:26:43,310 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, 100 00:26:47,820 --> 00:27:06,800 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 101 00:27:06,810 --> 00:27:08,870 Alejandro PEREZ: actually vanishes. 102 00:27:10,800 --> 00:27:11,500 Alejandro PEREZ: Yes, 103 00:27:12,080 --> 00:27:14,490 Eugenio Bianchi: yeah, yeah. The question is about 104 00:27:14,500 --> 00:27:18,160 Eugenio Bianchi: a thirty fifth theory, if you can you, 105 00:28:00,160 --> 00:28:09,039 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 106 00:28:20,120 --> 00:28:36,949 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 107 00:28:50,710 --> 00:28:52,070 Alejandro PEREZ: um 108 00:28:52,300 --> 00:29:00,600 Alejandro PEREZ: that the force has to depend intrinsically from the division of the particle. Only so 109 00:29:01,300 --> 00:29:19,519 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 110 00:29:19,530 --> 00:29:30,790 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 111 00:29:51,370 --> 00:30:01,789 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. 112 00:30:01,800 --> 00:30:02,630 The 113 00:30:02,640 --> 00:30:09,650 Eugenio Bianchi: Yeah, It sounds still like an F two, or it is an for a number of derivatives up to two. 114 00:30:29,590 --> 00:30:42,459 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. 115 00:30:43,290 --> 00:30:45,290 Eugenio Bianchi: I don't want to leave it like me, The model. 116 00:30:45,300 --> 00:30:46,250 Eugenio Bianchi: Okay, 117 00:30:46,310 --> 00:30:47,370 Eugenio Bianchi: Thank you. 118 00:30:47,570 --> 00:30:48,610 All right. 119 00:30:57,850 --> 00:30:58,690 I mean, 120 00:30:58,700 --> 00:31:01,830 Abhay Vasant Ashtekar: Eugenia was talking about divergence. But 121 00:31:01,860 --> 00:31:04,719 Abhay Vasant Ashtekar: this, this, this is this classical in that I'm: going to. 122 00:31:18,000 --> 00:31:18,889 Abhay Vasant Ashtekar: Okay. So it 123 00:31:18,900 --> 00:31:19,600 Abhay Vasant Ashtekar: Yeah, 124 00:31:20,630 --> 00:31:28,320 Alejandro PEREZ: All right. So just one last thing about this, which is still part of the interaction. 125 00:31:42,600 --> 00:31:52,289 Alejandro PEREZ: The thing is that this friction effect on this current is, I mean, introduces a Lorentz violation 126 00:31:52,700 --> 00:32:12,919 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, 127 00:32:13,070 --> 00:32:19,480 Alejandro PEREZ: and the force or the divergence, I mean the force, the friction force. It produces tolerance, violation 128 00:32:41,100 --> 00:32:43,340 here. This this um. 129 00:32:51,120 --> 00:33:08,199 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 130 00:33:08,210 --> 00:33:14,389 Alejandro PEREZ: are just so suppressed by the scalar curvature in normal situations, 131 00:33:14,400 --> 00:33:24,159 Alejandro PEREZ: that this Lawrence violating terms would pass all the tests that we know that look for Lawrence, violation in volatility. 132 00:33:38,130 --> 00:33:47,889 Alejandro PEREZ: All right, So these ends, these are all things. And this ends the introduction kind of because I one more 133 00:33:59,130 --> 00:34:02,909 Alejandro PEREZ: interactions with matter. It could also decay 134 00:34:03,030 --> 00:34:10,610 Alejandro PEREZ: an exotic process where energy actually in matter, degrees of freedom is produced. 135 00:34:11,420 --> 00:34:25,160 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. 136 00:34:25,170 --> 00:34:41,089 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. 137 00:34:41,100 --> 00:34:41,589 It's a 138 00:34:41,600 --> 00:34:43,489 Alejandro PEREZ: the the thing I want to. 139 00:36:11,060 --> 00:36:28,110 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 140 00:36:43,300 --> 00:36:53,619 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. 141 00:37:08,170 --> 00:37:13,850 Alejandro PEREZ: The inflation and the main difference is that from the very beginning the 142 00:37:47,770 --> 00:37:57,230 Alejandro PEREZ: unsettled conceptual discussions here. The point of view is that at the plank scale in blue quantum gravity, for example. 143 00:38:18,310 --> 00:38:23,789 Alejandro PEREZ: So these are all words. Now, i'm going to try to give you more details about the construction of this model. 144 00:38:25,020 --> 00:38:30,810 Alejandro PEREZ: Right? So, as I said, we postulate because vertical, constant to start off at the 145 00:38:31,890 --> 00:38:35,140 Alejandro PEREZ: the natural planks scale into the cave 146 00:38:35,200 --> 00:38:37,799 Alejandro PEREZ: exponentially with some 147 00:38:47,790 --> 00:38:49,899 Alejandro PEREZ: in a time. T. 148 00:38:49,970 --> 00:38:54,889 Alejandro PEREZ: Which is this preferred time of minimal gravity. In the context of cosmology, 149 00:39:05,010 --> 00:39:08,909 Alejandro PEREZ: then something that decays exponentially in you of all time. You 150 00:39:09,080 --> 00:39:18,710 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 151 00:39:19,110 --> 00:39:22,579 Alejandro PEREZ: you know the postulated exponential decay. 152 00:39:29,960 --> 00:39:43,630 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 153 00:39:43,660 --> 00:39:48,539 Alejandro PEREZ: is defined by this preferred volume, structure of universal gravity. The 154 00:39:57,600 --> 00:40:03,619 Alejandro PEREZ: looks like this one. So you have a very slow decay, and when you 155 00:40:03,900 --> 00:40:17,799 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. 156 00:40:23,810 --> 00:40:29,400 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. 157 00:40:29,410 --> 00:40:34,879 Alejandro PEREZ: Yeah, there has to be matter to use a freedom because because 158 00:40:36,930 --> 00:40:46,779 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. 159 00:40:47,570 --> 00:40:53,839 Abhay Vasant Ashtekar: So for this, for what I mean, I mean, like the matter of that kind of freedom and robbers and Walker. 160 00:40:53,860 --> 00:41:00,290 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? 161 00:41:27,480 --> 00:41:34,990 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? 162 00:41:42,590 --> 00:41:48,150 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. 163 00:41:48,400 --> 00:42:05,369 Abhay Vasant Ashtekar: Yes, but because we are doing some. 164 00:42:05,750 --> 00:42:09,150 Alejandro PEREZ: Yeah, I would say I I think it will write it explicitly in the next slide. 165 00:42:09,540 --> 00:42:17,389 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 166 00:42:17,910 --> 00:42:27,909 Ivan Agullo: number of defaults that we call an end. So basically beta can be trained with is an end. 167 00:42:28,150 --> 00:42:39,750 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, 168 00:42:41,580 --> 00:42:48,869 Ivan Agullo: it was. You are a gill. I I was asking something that you are explaining now. So forget about it. 169 00:42:48,880 --> 00:42:52,690 Laurent Freidel: Okay, I do have. I do have a question uh, 170 00:42:52,700 --> 00:42:53,959 Laurent Freidel: and you know, 171 00:42:53,970 --> 00:43:01,989 Laurent Freidel: So it's because if the matter is the usual matter, then it's energy, momentum, cancer is conserved. But then, you 172 00:43:02,000 --> 00:43:08,949 Laurent Freidel: that so? You want to change the conservation of energy, and you know momentum, so then 173 00:43:09,160 --> 00:43:19,949 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. 174 00:43:35,380 --> 00:43:44,440 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. 175 00:43:44,680 --> 00:43:47,330 Alejandro PEREZ: It wouldn't be conserved if it's coupled 176 00:43:47,450 --> 00:43:50,950 Alejandro PEREZ: with this underlying granular. 177 00:44:33,180 --> 00:44:50,289 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. 178 00:44:55,100 --> 00:44:55,790 Alejandro PEREZ: Yeah. Yeah. 179 00:44:55,800 --> 00:45:13,079 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 180 00:45:13,150 --> 00:45:14,430 Alejandro PEREZ: with 181 00:45:15,100 --> 00:45:26,099 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. 182 00:45:26,110 --> 00:45:28,869 Alejandro PEREZ: Okay, like, you know, like um. 183 00:45:34,650 --> 00:45:52,489 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 184 00:46:03,370 --> 00:46:23,990 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. 185 00:46:24,000 --> 00:46:24,790 Okay, 186 00:46:24,800 --> 00:46:32,400 Alejandro PEREZ: which has to do with the fact that our space-time being smooth and to all scales is only an approximation. 187 00:46:34,080 --> 00:46:49,030 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 188 00:46:49,270 --> 00:46:55,890 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, 189 00:46:55,900 --> 00:46:59,290 Alejandro PEREZ: you're changing. You're relaxing that condition by having a right-hand side 190 00:47:09,600 --> 00:47:11,390 Alejandro PEREZ: a of all this. Right? 191 00:47:11,400 --> 00:47:13,790 Laurent Freidel: Yeah, Yeah, they Are you talking about? 192 00:47:24,300 --> 00:47:43,590 Laurent Freidel: Yeah. And you're saying that the 193 00:47:44,030 --> 00:47:53,420 Alejandro PEREZ: you need to add all the ideas of fields that interact with electric and magnetic fields to have a diversions free. So 194 00:47:54,250 --> 00:48:01,970 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. 195 00:48:02,800 --> 00:48:13,879 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 196 00:48:13,890 --> 00:48:16,379 Laurent Freidel: is that is that your assumption, or 197 00:48:16,500 --> 00:48:26,189 Alejandro PEREZ: is on a mechanical. But I don't see the argument why it has to be. 198 00:48:26,200 --> 00:48:42,259 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, 199 00:48:42,270 --> 00:48:52,839 Alejandro PEREZ: this would produce this type of effects. Of course you could have some model of dark matter, and I believe they are. 200 00:48:52,850 --> 00:49:08,119 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 201 00:49:08,130 --> 00:49:24,430 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 202 00:49:24,440 --> 00:49:32,770 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. 203 00:49:32,990 --> 00:49:35,479 Abhay Vasant Ashtekar: But in my 204 00:49:35,490 --> 00:49:37,090 Abhay Vasant Ashtekar: in my mind 205 00:49:37,100 --> 00:49:37,850 it's 206 00:49:38,030 --> 00:49:48,890 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 207 00:49:48,900 --> 00:49:53,069 Abhay Vasant Ashtekar: you write down this equation So that question implicitly, I that there is a metric. 208 00:49:53,630 --> 00:49:56,430 Abhay Vasant Ashtekar: The statement is that if there is a metric, 209 00:49:56,680 --> 00:50:15,380 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, 210 00:50:15,390 --> 00:50:16,859 Abhay Vasant Ashtekar: then it must be conserved 211 00:50:58,900 --> 00:51:02,419 that diversions of the team menu of the standard model is zero. 212 00:51:02,490 --> 00:51:04,170 Alejandro PEREZ: Okay, It's all in time. 213 00:51:04,180 --> 00:51:05,439 Alejandro PEREZ: Okay, Yeah, 214 00:51:08,780 --> 00:51:11,949 Alejandro PEREZ: All right. So. But okay, So 215 00:51:12,550 --> 00:51:18,899 psingh: don't want to get stuck in this slide. I have given this. 216 00:51:19,140 --> 00:51:20,500 psingh: Yeah, 217 00:51:20,560 --> 00:51:29,640 psingh: Alex: I'm: sorry. Like, like. My question is exactly about this slide. So in the not in the 218 00:51:39,810 --> 00:51:46,329 psingh: Yes, it grows again. So this period is when the cosmological, constant decays exponentially. 219 00:51:46,360 --> 00:52:05,140 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. 220 00:52:05,150 --> 00:52:07,800 psingh: What I don't understand is that when you have this 221 00:52:07,960 --> 00:52:22,000 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? 222 00:52:22,340 --> 00:52:37,470 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 223 00:52:37,570 --> 00:52:44,839 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 224 00:52:46,050 --> 00:52:49,189 Alejandro PEREZ: I completely understand your questions. So let me answer the question you. 225 00:53:03,400 --> 00:53:18,520 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 226 00:53:47,800 --> 00:53:51,410 Alejandro PEREZ: yeah, I do have them there, and we're going to get to the questions 227 00:54:02,270 --> 00:54:05,310 Alejandro PEREZ: sending energy into the radiation. 228 00:54:05,410 --> 00:54:07,229 Alejandro PEREZ: Now, at the beginning 229 00:54:07,730 --> 00:54:09,240 Alejandro PEREZ: the beginning. 230 00:54:09,250 --> 00:54:10,750 Alejandro PEREZ: Ah, there! 231 00:54:26,500 --> 00:54:27,439 Alejandro PEREZ: Okay. 232 00:54:27,580 --> 00:54:31,259 Alejandro PEREZ: So at the beginning you have an exponential expansion 233 00:54:31,390 --> 00:54:43,499 Alejandro PEREZ: that is so violent that, as usual, inflationary cosmology dibutes exponentially, the radiation so radiation goes like one over eight to the 234 00:54:52,600 --> 00:55:12,529 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. 235 00:55:12,540 --> 00:55:15,289 Alejandro PEREZ: They are Also, I mean, all this is New Mexico. 236 00:55:15,300 --> 00:55:21,890 Alejandro PEREZ: We have to do a numerical calculation to actually solve the Friedman equations and the modifying calculations. 237 00:55:21,900 --> 00:55:32,140 Alejandro PEREZ: However, you can just do some seminolithic approximations that actually lead to these statements that I have written in the picture. 238 00:55:32,150 --> 00:55:50,770 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. 239 00:56:28,930 --> 00:56:38,590 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 240 00:56:53,000 --> 00:57:00,629 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. 241 00:57:13,230 --> 00:57:24,870 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, 242 00:57:29,500 --> 00:57:47,309 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. 243 00:58:14,020 --> 00:58:21,050 Alejandro PEREZ: But there is a source to radiation, and this source is the one that we modify the behavior of radiation with scale. 244 00:58:21,910 --> 00:58:23,680 Alejandro PEREZ: So you can solve everything. 245 00:58:23,690 --> 00:58:31,799 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, 246 00:58:31,810 --> 00:58:51,329 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, 247 00:58:51,450 --> 00:59:10,660 psingh: the equation of State acts like minus two. So 248 00:59:40,800 --> 00:59:44,390 Alejandro PEREZ: it's totally not valid, because you are injecting energy into the system. 249 00:59:57,120 --> 01:00:00,559 Alejandro PEREZ: It's like having it on, and you are heating up the on. 250 01:00:03,500 --> 01:00:08,420 psingh: I think the problem is that probably you Won't interpret it exactly as radiation 251 01:00:18,600 --> 01:00:26,379 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 252 01:00:26,390 --> 01:00:27,259 again. 253 01:00:29,970 --> 01:00:33,589 psingh: Yeah, I think we should discuss discuss later. Thank you. 254 01:00:33,600 --> 01:00:34,810 Okay, 255 01:01:11,160 --> 01:01:18,380 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 256 01:01:18,920 --> 01:01:23,130 Alejandro PEREZ: two. Um! So you see here. Um, 257 01:01:56,680 --> 01:02:05,019 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 258 01:02:05,110 --> 01:02:09,179 Alejandro PEREZ: to order. It might use the same results with this spacing divide model. 259 01:02:10,720 --> 01:02:12,770 Alejandro PEREZ: All right. So 260 01:02:13,750 --> 01:02:29,390 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 261 01:02:29,400 --> 01:02:39,329 Alejandro PEREZ: when when one considers an interacting that energy through it, like the one I am considering that it 262 01:02:39,340 --> 01:02:58,690 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 263 01:02:58,700 --> 01:03:06,819 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 264 01:03:07,950 --> 01:03:13,309 Alejandro PEREZ: okay, so I can go to the key thing I wanted to tell you in the talk, 265 01:03:13,950 --> 01:03:21,989 Alejandro PEREZ: So we have, Therefore this model exhibits inflation for a certain number of efforts, 266 01:03:22,000 --> 01:03:23,539 Alejandro PEREZ: but there is no inflex on 267 01:03:48,820 --> 01:03:53,709 Alejandro PEREZ: so just a proof of concept. Is there another way of thinking about the 268 01:03:53,740 --> 01:03:56,149 Alejandro PEREZ: what we see at the Cmb. 269 01:04:19,290 --> 01:04:35,449 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. 270 01:04:53,160 --> 01:04:56,679 Alejandro PEREZ: Uh this granularity that actually breaks 271 01:04:57,090 --> 01:05:16,709 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 272 01:05:27,320 --> 01:05:29,229 Alejandro PEREZ: He's so. Ah, 273 01:05:55,680 --> 01:05:57,140 Alejandro PEREZ: but again 274 01:05:57,570 --> 01:05:59,359 Alejandro PEREZ: with the idea. 275 01:05:59,400 --> 01:06:07,909 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 276 01:06:07,920 --> 01:06:28,790 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 277 01:06:30,720 --> 01:06:33,470 Alejandro PEREZ: He's basically London. 278 01:06:35,730 --> 01:06:37,289 Alejandro PEREZ: My target is not 279 01:06:54,570 --> 01:07:13,080 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. 280 01:07:27,410 --> 01:07:34,889 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. 281 01:07:44,810 --> 01:08:01,720 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 282 01:08:01,730 --> 01:08:05,420 Alejandro PEREZ: would be the field theoretical degrees of freedom of the Higgs, K. 283 01:08:06,100 --> 01:08:16,540 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, 284 01:08:16,720 --> 01:08:20,829 Alejandro PEREZ: and so they would be in the motion eight is generated at the planning scale, 285 01:08:20,950 --> 01:08:24,290 Alejandro PEREZ: a very typical scale, which is the time scale. 286 01:08:30,700 --> 01:08:33,629 Alejandro PEREZ: But in homogeneities it's scaling. 287 01:08:44,340 --> 01:08:47,969 Alejandro PEREZ: However, we would see that because of the sitter expansion, 288 01:09:08,649 --> 01:09:18,660 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 289 01:09:26,520 --> 01:09:46,480 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. 290 01:09:55,750 --> 01:10:01,220 Alejandro PEREZ: These are the fluctuations of the heap Scalar and I'm going to assume that the first moments are zero 291 01:10:02,860 --> 01:10:11,889 Alejandro PEREZ: only we will only need to consider the second moments, and the second moments are included in the two-point correlation. Function. 292 01:10:11,900 --> 01:10:30,480 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 293 01:10:30,490 --> 01:10:32,250 Alejandro PEREZ: in it. 294 01:10:45,300 --> 01:10:58,899 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, 295 01:11:30,720 --> 01:11:32,590 Eugenio Bianchi: so, if you know the power spectrum, 296 01:11:32,600 --> 01:11:35,989 Alejandro PEREZ: you know the two-point function. If you know the two-point function, we know the power. Thank you, 297 01:11:36,000 --> 01:11:37,689 Alejandro PEREZ: or you have information about the power. Space. 298 01:11:49,870 --> 01:11:52,679 Alejandro PEREZ: I will answer the question in a moment 299 01:11:53,030 --> 01:11:54,830 Eugenio Bianchi: at Venezuela. 300 01:11:57,200 --> 01:11:59,160 Alejandro PEREZ: Okay, 301 01:12:05,540 --> 01:12:07,570 Alejandro PEREZ: uh energy momentum 302 01:12:08,490 --> 01:12:12,339 Alejandro PEREZ: contributions to out there the 303 01:12:12,350 --> 01:12:30,229 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 304 01:12:31,200 --> 01:12:46,940 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 305 01:13:21,040 --> 01:13:22,389 Alejandro PEREZ: inflation 306 01:13:33,230 --> 01:13:35,060 Alejandro PEREZ: very quickly go to zero. 307 01:13:35,540 --> 01:13:37,390 Alejandro PEREZ: So now, if you have, 308 01:13:37,920 --> 01:13:40,290 Alejandro PEREZ: you know the contribution, 309 01:14:02,080 --> 01:14:07,500 Alejandro PEREZ: the equation of state, the one that comes from diverges of T in your equal to zero, 310 01:14:08,410 --> 01:14:23,820 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. 311 01:14:23,830 --> 01:14:29,660 Alejandro PEREZ: This quantity depends only on the power spectrum of 312 01:14:29,820 --> 01:14:36,129 Alejandro PEREZ: perturbations of the heat scalar. So I can think of this work. 313 01:14:52,100 --> 01:15:03,089 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 314 01:15:03,190 --> 01:15:04,769 Alejandro PEREZ: the power spectrum. 315 01:15:06,780 --> 01:15:23,449 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 316 01:15:23,490 --> 01:15:29,980 Alejandro PEREZ: geometry, and therefore being hit by this granular structure. And so this 317 01:15:35,220 --> 01:15:46,960 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, 318 01:15:47,070 --> 01:16:06,709 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. 319 01:16:10,300 --> 01:16:15,099 Alejandro PEREZ: So this parameter gamma parametrizes how much energy 320 01:16:40,980 --> 01:16:59,049 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 321 01:17:06,140 --> 01:17:20,250 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, 322 01:17:20,960 --> 01:17:24,469 Alejandro PEREZ: and this would be a free parameter on our of our model. 323 01:17:25,100 --> 01:17:32,889 Alejandro PEREZ: This is what this This is an example of how this quantities depend on the power spectrum, 324 01:17:32,970 --> 01:17:34,559 Alejandro PEREZ: for example, 325 01:17:34,770 --> 01:17:36,590 Alejandro PEREZ: because 326 01:17:36,840 --> 01:17:54,689 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. 327 01:18:29,460 --> 01:18:32,099 Alejandro PEREZ: Okay, So we integrate from some. 328 01:18:39,400 --> 01:18:41,770 Alejandro PEREZ: So this equation that you have is 329 01:18:43,020 --> 01:18:44,510 Alejandro PEREZ: because 330 01:18:44,790 --> 01:18:48,210 Alejandro PEREZ: I don't know how. My, how am I doing on on time 331 01:18:51,230 --> 01:18:54,209 Jorge Pullin: while you've been on for an hour and twenty minutes already? 332 01:18:56,240 --> 01:19:04,640 Alejandro PEREZ: All right. Okay. So this equation is a function of the power spectrum that can be solved in this solution. 333 01:19:09,900 --> 01:19:15,699 Alejandro PEREZ: So maybe, in order not not to lose you all, I see that already, 334 01:19:15,710 --> 01:19:17,490 Eugenio Bianchi: Riandro at. 335 01:19:17,500 --> 01:19:29,569 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 336 01:19:34,850 --> 01:19:36,849 Alejandro PEREZ: yes. Um 337 01:19:41,670 --> 01:19:46,099 Alejandro PEREZ: um do. I have a simple answer. 338 01:19:46,370 --> 01:19:47,610 Alejandro PEREZ: Ooh! 339 01:19:57,620 --> 01:19:58,849 Eugenio Bianchi: We learn 340 01:19:59,260 --> 01:20:01,119 Eugenio Bianchi: inflationary cosmology. 341 01:20:01,130 --> 01:20:03,819 Alejandro PEREZ: It's not different. It's it's the right. 342 01:20:04,480 --> 01:20:07,389 Eugenio Bianchi: Do you agree with the mechanism, it's different. 343 01:20:07,400 --> 01:20:08,990 Alejandro PEREZ: Oh, yeah, yeah, the mechanism is different. 344 01:20:09,000 --> 01:20:20,470 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, 345 01:20:21,260 --> 01:20:29,700 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. 346 01:20:29,750 --> 01:20:31,649 Alejandro PEREZ: Well, this is not enough. 347 01:20:50,440 --> 01:20:53,040 Alejandro PEREZ: He's still guaranteed, i'm. 348 01:20:54,150 --> 01:20:58,289 Alejandro PEREZ: I'm sorry I don't have a simple, quite answer. But there is a simple answer. But 349 01:20:58,300 --> 01:21:01,089 Alejandro PEREZ: let me think about it, and I will write to you anymore. Okay, 350 01:21:01,100 --> 01:21:02,200 Eugenio Bianchi: thank you. 351 01:21:03,280 --> 01:21:08,750 Ivan Agullo: Can you also include me in the email. I think this is the most important part of the talk. 352 01:21:09,730 --> 01:21:10,690 Alejandro PEREZ: Okay? 353 01:21:10,700 --> 01:21:15,790 Ivan Agullo: Yes, of course I can include you in the in the email. Thank you. 354 01:21:26,200 --> 01:21:39,900 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, 355 01:21:42,510 --> 01:21:47,289 Alejandro PEREZ: all right. So one gets a skin invariant spectrum, 356 01:21:54,420 --> 01:21:57,889 Alejandro PEREZ: you know I I keep thinking about giving you the answer. Um, 357 01:21:59,430 --> 01:22:13,189 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 358 01:22:13,200 --> 01:22:31,060 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, 359 01:22:39,840 --> 01:22:42,170 Alejandro PEREZ: and for that you could use 360 01:22:43,670 --> 01:22:53,100 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 361 01:23:09,340 --> 01:23:18,640 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. 362 01:23:18,650 --> 01:23:36,960 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 363 01:23:37,120 --> 01:23:56,709 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. 364 01:23:57,270 --> 01:24:16,179 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. 365 01:24:16,190 --> 01:24:23,529 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 366 01:24:49,410 --> 01:24:55,750 Alejandro PEREZ: due to its self interaction potential. And so this lambda that you see here for the first time. 367 01:24:55,960 --> 01:25:02,020 Alejandro PEREZ: In fact, I should have said you saw it before, too, is actually the lambda that appears in front of the 368 01:25:03,120 --> 01:25:08,580 Alejandro PEREZ: the fight to the fourth term. In the potential of the heats 369 01:25:17,930 --> 01:25:26,529 Alejandro PEREZ: the deviations from scaling lines are directly tied to the self-crapping of the heaps. And so observations require the amplitude of 370 01:25:26,640 --> 01:25:30,290 Alejandro PEREZ: this to be something. This is what observations 371 01:25:56,090 --> 01:26:03,270 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 372 01:26:03,460 --> 01:26:15,320 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. 373 01:26:32,870 --> 01:26:55,630 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 374 01:27:12,600 --> 01:27:16,589 Alejandro PEREZ: aviation or scale lines, we can also compute the next 375 01:27:16,600 --> 01:27:20,330 Alejandro PEREZ: correction, and we find for this quantity 376 01:27:37,000 --> 01:27:39,469 Alejandro PEREZ: the so the model 377 01:27:45,600 --> 01:27:46,090 it's a, 378 01:28:09,930 --> 01:28:25,710 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. 379 01:28:33,240 --> 01:28:42,189 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. 380 01:28:42,200 --> 01:29:01,349 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 381 01:29:02,330 --> 01:29:18,809 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 382 01:29:23,760 --> 01:29:43,730 Alejandro PEREZ: the temperature, then you have a natural generation of dark matter in terms of memorial black holes, 383 01:29:53,810 --> 01:30:13,770 Alejandro PEREZ: the that would lead naturally to inflation, and with that, with natural conditions and some strong assumptions, I read 384 01:30:26,620 --> 01:30:44,420 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 385 01:30:44,540 --> 01:30:45,889 Alejandro PEREZ: at higher spheres, 386 01:30:45,900 --> 01:30:56,970 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. 387 01:30:57,420 --> 01:31:13,129 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 388 01:31:16,750 --> 01:31:18,219 Alejandro PEREZ: it's all. 389 01:31:18,300 --> 01:31:37,490 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. 390 01:31:45,440 --> 01:32:02,660 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 391 01:32:03,390 --> 01:32:04,849 Alejandro PEREZ: and the Us. 392 01:32:04,890 --> 01:32:09,430 Alejandro PEREZ: Thank you for your patience, and thank you very much for your pleasure. 393 01:32:14,100 --> 01:32:15,910 Jorge Pullin: Any questions left? 394 01:32:16,690 --> 01:32:32,449 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 395 01:32:46,050 --> 01:32:47,870 Alejandro PEREZ: Um: 396 01:32:51,270 --> 01:32:59,590 Alejandro PEREZ: yes. Okay. So here we do have inflation. We have a face that lasts for sixty falls about sixty falls of the 397 01:32:59,890 --> 01:33:02,320 Alejandro PEREZ: of the reputation 398 01:33:02,410 --> 01:33:04,219 Alejandro PEREZ: of exponential 399 01:33:04,230 --> 01:33:07,529 Alejandro PEREZ: expansion. But of course we assume we 400 01:33:23,260 --> 01:33:35,280 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 401 01:33:35,420 --> 01:33:53,189 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 402 01:33:53,200 --> 01:33:57,980 Alejandro PEREZ: inflation. But for the very same reasons or as inflation, 403 01:34:06,250 --> 01:34:09,460 Alejandro PEREZ: it's just insensitive to 404 01:34:16,560 --> 01:34:18,420 Alejandro PEREZ: so um 405 01:34:34,650 --> 01:34:47,890 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, 406 01:35:07,080 --> 01:35:08,709 Alejandro PEREZ: but I might be 407 01:35:09,380 --> 01:35:11,960 Alejandro PEREZ: naive. I know. 408 01:35:13,660 --> 01:35:15,179 Jorge Pullin: Okay, Western. 409 01:35:15,470 --> 01:35:23,810 Western: Yeah, Thank you, Alex. Actually, your Toko was very dense. Full of things. Bit are the 410 01:35:23,820 --> 01:35:44,880 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, 411 01:35:44,890 --> 01:36:14,179 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 412 01:36:14,190 --> 01:36:33,500 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 413 01:36:33,510 --> 01:36:44,270 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 414 01:36:44,280 --> 01:37:00,919 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 415 01:37:00,930 --> 01:37:16,550 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 416 01:37:17,040 --> 01:37:19,469 Alejandro PEREZ: Moscow. 417 01:37:58,080 --> 01:38:04,869 Alejandro PEREZ: But why not? And so here. We observed that if there were such things like plank Mass: 418 01:38:15,050 --> 01:38:41,190 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. 419 01:38:41,200 --> 01:38:48,979 Western: Yeah, using the terminology of people, Your black hole for something that has to plan for us is not a good idea 420 01:38:49,520 --> 01:38:59,589 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 421 01:39:04,910 --> 01:39:16,490 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 422 01:39:17,820 --> 01:39:19,480 Western: Thank you. 423 01:39:19,730 --> 01:39:20,900 Jorge Pullin: I'm. By 424 01:39:24,030 --> 01:39:37,340 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, 425 01:39:48,500 --> 01:40:04,729 Abhay Vasant Ashtekar: but the running of the coupling is 426 01:40:05,270 --> 01:40:15,169 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 427 01:40:15,180 --> 01:40:33,249 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 428 01:40:33,690 --> 01:40:53,230 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 429 01:40:58,760 --> 01:41:12,210 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, 430 01:41:12,690 --> 01:41:20,090 Abhay Vasant Ashtekar: exactly that reason you have to make all kinds of assumptions right? And so do you agree that 431 01:41:21,960 --> 01:41:30,589 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. 432 01:41:30,600 --> 01:41:39,789 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 433 01:41:39,800 --> 01:41:49,350 Abhay Vasant Ashtekar: no, no, but the actual formation. The mechanism for structural formation is the same as usual information. 434 01:41:50,010 --> 01:41:51,890 Alejandro PEREZ: And so people 435 01:41:51,900 --> 01:42:10,990 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. 436 01:42:21,230 --> 01:42:23,730 Abhay Vasant Ashtekar: The same assumption there. So it's not there. 437 01:42:23,740 --> 01:42:25,329 Abhay Vasant Ashtekar: They have to. 438 01:42:25,340 --> 01:42:38,890 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. 439 01:42:39,180 --> 01:42:40,990 Abhay Vasant Ashtekar: It seems to be that it 440 01:42:41,000 --> 01:43:01,720 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 441 01:43:19,430 --> 01:43:35,380 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. 442 01:43:54,550 --> 01:43:55,570 Jorge Pullin: Can you? 443 01:43:56,000 --> 01:43:58,690 Eugenio Bianchi: Yeah, thanks for that. 444 01:44:06,870 --> 01:44:09,740 Eugenio Bianchi: There's a formula there in a box. 445 01:44:15,430 --> 01:44:16,899 Eugenio Bianchi: Yes, this one. 446 01:44:32,330 --> 01:44:51,399 Eugenio Bianchi: So you have the statement, and this one matrices observations beautifully. I don't follow all the steps of how you 447 01:44:51,610 --> 01:44:54,490 Eugenio Bianchi: This is an observation. Okay, it's not. 448 01:44:54,500 --> 01:44:55,790 Alejandro PEREZ: It's an observation 449 01:44:55,800 --> 01:45:06,689 Eugenio Bianchi: that makes the value of gamma that I need to fit observations 450 01:45:06,700 --> 01:45:18,780 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 451 01:45:18,910 --> 01:45:21,989 Alejandro PEREZ: controls the coupling between the granular and 452 01:45:22,000 --> 01:45:25,579 Alejandro PEREZ: and and in the low energy 453 01:45:25,590 --> 01:45:38,200 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. 454 01:45:49,650 --> 01:45:51,840 Alejandro PEREZ: No, I don't think so, 455 01:45:52,510 --> 01:46:11,650 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. 456 01:46:16,200 --> 01:46:19,890 Eugenio Bianchi: Yeah, this I understand that. So the question was, If there's some 457 01:46:39,230 --> 01:46:43,020 Abhay Vasant Ashtekar: from the scheme, you add in part, it is a ratio Gamma or Lambda Square the 458 01:46:43,210 --> 01:46:58,390 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 459 01:47:05,840 --> 01:47:07,769 Alejandro PEREZ: Gamma appears here. 460 01:47:19,710 --> 01:47:21,620 Abhay Vasant Ashtekar: Yeah, but this is a free parameter, 461 01:47:29,280 --> 01:47:32,230 Alejandro PEREZ: and in in the he that's what I would say. 462 01:47:51,930 --> 01:48:02,990 Abhay Vasant Ashtekar: Everything is meeting up. Thank you very much for the impatient. I. We use this stochastic 463 01:48:03,000 --> 01:48:07,440 Alejandro PEREZ: to in this reasoning of energetics. 464 01:48:18,040 --> 01:48:29,580 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 465 01:48:29,650 --> 01:48:30,880 Alejandro PEREZ: it's 466 01:48:41,800 --> 01:48:51,639 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 467 01:48:51,750 --> 01:48:59,590 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. 468 01:48:59,600 --> 01:49:07,120 Abhay Vasant Ashtekar: I agree to some extent. But what I want to say is that the vacuum in quantum field theory 469 01:49:21,600 --> 01:49:37,890 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, 470 01:49:46,520 --> 01:49:49,190 Alejandro PEREZ: to begin with. Why, in the standard picture. 471 01:49:49,200 --> 01:49:52,490 Alejandro PEREZ: We have the bunch, David Vacuum, which is homogeneous and isotropic. 472 01:50:05,100 --> 01:50:08,959 Abhay Vasant Ashtekar: Yeah, that's that's a it's not related to your talk. So thank you. 473 01:50:10,450 --> 01:50:12,439 Jorge Pullin: If the includes Tanker, the handwriting. 474 01:50:13,300 --> 01:50:14,630 Thank you and the group. 475 01:50:14,870 --> 01:50:16,550 Alejandro PEREZ: Thank you. Thank you.