Leonard Susskind - Eternal Inflation & De Sitter Space

was only 40 70 now let's come to the present witness 56 called risky is 53 win day one of the dominators of cosmology of 16 may I happen to be 68 our glue to 60 and now all the Lincoln is this have wonderful resonate that means that people are going on for long well I'm afraid that they need something very bad what I'm afraid is happening and it troubles me is as we all know science by its very nature is revolution and rebellion still happening I think it's time young people that new push us off the stage my opinion is the truth but it'll happen nature will take care of it I want to talk about eternal life one of the ways of thinking about it all right so I'm used to talking in this subject to an audience of cosmologists or people who have been interested in cosmology for a while and they all recognize this picture instantly does everybody recognize it anybody not okay so this is a picture of what happens in an eternal inflating Universal for you very quickly what it means the purple region here is the sitter space if I draw the sitter space is a conformal diagram then it has a space like boundary the space like boundary is time equals infinity that's the conformal structure of the theory the lower part is the sitter space if bubbles nucleate in in the sitter space the pseudo space is metastable which many of us think it ought to be if the sitter space is metastable if you're alone lower energy vacuums and strain theory we know there are lower energy vacuums both flat supersymmetric vacuums and if I consider vacuums then bubbles can nucleate this represents the nucleation of a bubble bubble of those outlets be wiped all practical purposes and I've drawn here basically a picture which would correspond to the nucleation of a bubble with exactly zero cosmological constant if it didn't have exactly zero Y zero cosmological constant well if you're familiar drawing conformal diagrams dispenses you know that flat space as a future infinity which looks like this and what I've basically done here is cut out a piece of them of the center space and patched in piece of black space and that's the kind of thing that you see we have Oh nucleation to a black space but flat space I merely mean that the asymptotic vacuum energy goes to zero I don't necessarily mean that it's exactly flat space but asymptotically late time that the the cosmological vacuum the cosmological constant goes to zero if the cosmological constant didn't go to zero as in our own space-time or come back to that later if I have chance then this would be rounded out a little bit but in fact if you actually drew it for our own space time because our cosmological constant is so small it would almost look exactly like this with you would need well I would say probably the roundedness over here on this screen would probably involve a deviation something like about one plunk unit of a height here so there is not very it doesn't change it very much so I'm going to pretend that the world has absolutely zero cosmological constant we'll come back to the implications of a real cosmological constant later in string theory and I suspect in any theory the only vacuums with absolutely zero cosmological constants are probably super symmetric so if we really have to try to do this we will be stuck with super symmetric vacuums and so be it let's study the cosmology of the nucleation of a world with zero cosmological constant that's the exploration that I want to do today what how do we describe how do we mathematically describe how do we put together all the elements that we've learned over the last ten years and so forth some from string theory some from some from the holographic principle some from black hole ideas how do we describe the world inside this nucleated bubble let us see what button do I push to go through the next one this one oh yeah that was good let me go back though first what's this horizontal line and why do I draw it well the usual way of thinking about space-time is to foliate it with space like surfaces and imagine quantum states on the first-base like surfaces and then push them forward with some kind of Hamiltonian this is a very dangerous thing to do in space times not so much a dangerous thing with something that's going to do it one has to do it with great care in order not to over count if the space-time has horizons and the sitter space in particular there's all kinds of horizons in this space here an observer looking from here or an observer down here somewhere else cannot see out beyond this light cone here and so there are all kinds of horizons there and the reason I bring that up is because a lot of the questions which have to do for this kind of eternal inflation this is eternal inflation are in between these interstitial spaces in here between these bubbles the vacuum considered continues to be the sitter there's more and more volume in them and more and more room for more and more bubbles to nucleate I forgot what I was going to say it's let's just go on yeah oh yes the point is that one of them chief problems that people who think about eternal inflation this way come up against is the counting of vacuums it's called the measure problem how do you count how do you put statistics on this and if you're gonna do it right you better be very very careful about over counting and counting correctly the number of degrees of freedom the number of the number of possibilities and so forth and that can get problematic particularly in the context of horizons and I Illustrated for you from a web very well-known example the example of a black one of the things we found from starting with bekenstein or to Hawking learning all about the information problem in black holes and so forth is that we should not think of the degrees of freedom behind the horizon in front of the horizon as being independent of each other they're complementary descriptions of the same thing in the sense that the hawking radiation which is carried off by the particles of the evaporation products carry exactly the same information as the information that we would normally think is behind the horizon any other counting would over count and would lead to this disastrous conclusion that information is lost behind the horizon so this is something we have learned from black holes and it has taught us not to try to think simultaneously behind the horizon in front of the horizon I don't know precisely what the lesson is for cosmology but I would suggest the safest thing to do the safest thing to do which probably is closest in spirit that thinking about the black hole from outside the horizon consistently would be to take the causal patch of the top of his diagram here the top of the diagram is time like infinity the causal patch of such a diagram and a causal patch now means simply the backward light cone for the black hole the causal patch of future infinity would be the backward light cone of the point up at the top here but take the black backward light cone which is all the points which can be seen by a late time observer here and restrict the tension to them so that is exactly what I'm going to do I'm going to study basically the physics within one patch like this what does an observer in there see now of course an observer in there pretty much constitutes all of ordinary cosmology starting from the bubble nucleation all right um one of the other things we've learned over the last decade or so more than last decade is the holographic principle in particular we learned that more strongly in the context of anti-de sitter space I will come back to anti the sitter space but basically what it says again it's a counting problem it's very closely related to the counting problems of horizons is that if we have a volume of space filled with the universe ordinarily we would expect the number of possibilities the number of degrees of freedom the number of orthogonal states and so forth to be proportional for the volume of the space and one of the things we've learned is that that cannot be true simply because most of those possibilities would correspond to a black hole bigger than the region was studying and we've learned that the number of orthogonal degrees of freedom the number of orthogonal states of the system is proportional for the exponential of the area not the volume that's of course the holographic principle and that holographic principle in the context of anti-de sitter space has led to the idea of a duality between field theory on a boundary and bulk physics and I want you to just keep that in mind as we go along that should be we should take that into account with any kind of consistent precise description of our world and let me come to the question of why we have had so much trouble using in particular string theory but I think more generally than that why we've had such trouble trying to think about cosmology and I would say there really is no string theoretic framework at present that describes any interesting cosmological background I think it's quite closely related to the questions that we have asked about about background independence and so forth this is just another way of saying the same thing but Fellini's let me spell it out the string theory and I suspect more than just string theory can be very effective in describing a class of backgrounds which I call asymptotically cold asymptotically cold means all of the matter is localized is a finite amount of it it's localized in some finite you know space and as you move away you come to some very frozen extremely definite background which doesn't fluctuate very much in fact which doesn't fluctuate at all example would be flat space of course you're allowed to throw in us a handful of particles they're allowed to throw in a handful of particles from infinity a small number a small number means a finite number and then you can talk about an S matrix but you don't want to fill up the space with particles because then you don't have sensible a seems sensible from the point of view of an S matrix essentially a sensible background same thing is true of anti-de sitter space it's also asymptotically cold or asymptotically frozen and the reason is that it just takes an ever-increasing infinite amount of energy to bring a particle for the boundary so if you put in a certain amount of matter or certain find that amount of energy it will tend to drift to the center the boundaries being completely frozen okay that's exactly what's not true for any interesting cosmology first of all for closed cosmologies there are no asymptotic boundaries period for opening cosmologies which I will be interested in particular open frw open means negatively curved frw k equals -1 or for that matter for flat frw space is filled with particles space is filled with particles out for the asymptotic boundaries that's the assumption of homogeneity of course and as far as we can tell space is homogeneous and that means that there will be fluctuations for example I'm not talking about CMB fluctuations now they made it and it may include those but in general there will be fluctuations due the fluctuations in the matter of fluctuations in the in the temperature it's like fluctuations in whatever just fluctuations in the positions of particles there will be fluctuations not only in the ordinary things but even in the geometry of the boundary the geometry of the boundary will also fluctuate and that means that in cosmology we are not working in some fixed frozen boundary with some fixed frozen backgrounds exclusive that excuse me that I think is the primary reason why we we as string theorists we I don't know if you're a string theorist I don't even like the term string theorists but we have had no real success in finding a framework for for cosmology in the context of string theory what I'm going to do is try to show you a possible framework and the possible framework is based on the study of a cosmology within a bubble within a nucleated bubble and to try to understand how to describe it holographically and in a way that might be susceptible through the string theoretic description and so forth but for today I'm not even going to talk very much about string theory all right the basic working tool of studying the creation of a nucleated bubble is instant pons Coleman the lucha instant phones Coleman the lucha instant tongs are Euclidean geometry which have a topology of a 4 sphere the Euclidean geometry and Euclidean solutions of equations of motion including maybe some scalar fields and so forth and they have the topology of a 4 sphere but a deformed 4 sphere which instead of having oh 5 symmetry for sphere would have over 5 symmetry they have only o 4 symmetry and the simplest example would be called the thin wall approximation where you connect a de sitter vacuum the Euclidian description of a visitor vacuum as a sphere you've clearly you've connected through a completely flat vacuum on this side this would be the Coleman de lucha instant time for a transition from addis it of vacuum for a completely bath a flat vacuum slicing until the middle corresponds to P equals 0 or corresponds to the symmetry point in the Coleman dilution and farm and if you then go and try to make the Minkowski continuation of this you do it as follows you take the surface the symmetry surface here and you simply draw it over here starting at this end corresponds to starting at this pole of the sphere and going around to here for the pole with the center over here corresponds to this point over here so this surface is fully identical exactly as a space-like surface for what you would see if you slice the CBL instant-on right through the center but then instead of evolving it away from here with the euclidean equations of motion you evolve it with the Minkowski equations of motion what happens is you create a figure that looks something like this with flat space in here in the dark regions flat space-time in here in the dark region I'll just remember I will just remind you full flat space this entire triangle will be dark but instead it is now filled in in here with the sitter space if you like this is the nucleation point of a bubble only half of this diagram is really relevant for the bubble nucleation you can forget the other half Obama the pop 1/2 is relevant and this figure in here is the nucleated bubble that took place in the background of the de sitter space the symmetry group O 4 becomes oh 3 1 under the continuation what is oh 3 1 will will come to what oh 3 1 is but all 3 1 is a non compact group which whose orbits move you around in the space-time their space like in the bubble like also in this bubble time like in this part of the geometry in this diamond and also space like out here near the end of the de sitter era all right but we're going to be mainly in here and so you can see that the space like orbits of the symmetry group really stand for nothing but translational symmetry well not exactly translation symmetry because the space in here is not flat space as a flat space we'll see what it is in a moment but it's basically the translation of space inside the bubble the intersection over here where the future of the bubble intersects the decision region I'm just going to call Sigma but you can see what it means from somebody inside the bubble they're just looking out to space like infinity space like and who a couple will come back to this geometry in a moment let's yeah ya know it's kind of interesting the physics inside is following a finite universe things would be receptive oh you're inside a bottle but in fact it's a infinite negatively curved frw here on the tree equals minus 1 negative curve in the infinite why is that well if you draw the space like hyper surfaces that correspond through fixed for example if it was a scalar field which nucleated this transition here then these would be surfaces of homogeneous scalar field both space like surfaces those space like services in fact they are space like surfaces on which the symmetry group acts though space like surfaces are infinite and the reason is very simple the metric diverges up in these corners here and factor metric diverges all along here the metric is conformal diagrams if it's squished that diverges in here and the result is that these space hard surfaces are infinite they're homogeneous and a hyperbolic plane which means spaces of uniform negative curvature here is the metric eleska get the term well your honor memorize the metric for distillation it's just ordinary frw the T squared was aft squared and this metric here is the metric of space it's the metric of a hyperbolic geometry you would tell us hyperbolic because of the Cinch here it was flat space it would just be R squared but uniform negative curvature as a sin squared so the volume element increases rapidly this is just a two sphere and roughly speaking it corresponds to the two sphere of the sky when the observer at the centre works around this is the 2-sphere that he sees around so this is the metric that we'll be interested in and over here I've rewritten it trivially by replacing the time variable by conformal time that simply means that you replace little T by big things such that little BT squared is a of P squared 150 squared standard operation and if you do so then the coefficient of the BT square and is the R squared will be the same and then you can work in terms of P plus R and P - R those are kind of like comb coordinates T plus increases as we move outward away from the center the central observer here and T - varies along basically along this surface here that's what T plus is the - are just keep them in mind because all is this is this metric that you're describing here is this in the dark region of that diagram or is it region diagram drawn yeah this is only this is in the in the bottle in the green region in a previous diagram you had a dark region mmm I'm trying to connect this picture to the previous one right there so all right it's symmetric in here in this okay founded by a white cone in the past and bounded by a light cone future you shoot a special way to forgive this pace with slices pajama are there other formations with something like flats no negative courage and that's the only way you can really forgive this is pretty much the only particular if there were scalar field driving all of this then the scale of Y will be uniform of our surfaces if they were particles produced and generally would be particles produced temperatures and energy than densities with the uniform over surfaces so there is a symmetry taking you from point to point the poster whistles ok let me just tell you wanted to remarks about the scale factor if the cosmological constant is zero at late times then the scale factor at both early and late times simply varies as P itself small T that you can work out very easily and it implies that aim of compass say made but not the argument is conformal time conformal time a goes is the exponential of T V now let's read the simplifies the metric particularly if you go to length time and large R remember R is R is comoving distance coordinate distance out to a certain special point our preserve the spatial distance here is automatic looks like remember there was the T squared minus the R squared multiplied in scale factor here pinkie swear - the R squared just becomes DT plus DT - and then let me go back a step ok notice what was here there was the T plus DT minus x am T squared ok AFP's exponential equal but then for large our cinch our square becomes e to the to our so we get e to the two T from here each of the two far from here and the net result is that the coefficient of the 2-sphere method is e to the 2t plus alright as various as you move out along the T plus direction now let me come to what the census taker readings the census paper was originally introduced as an idea but it's basically by Steve Pinker in an unpublished article which has never been published and never will be published but it's essentially at least the terminology you certainly do the state Shanker I won't take responsibility for it but the basic idea had to do with looking back we're going to come back cause we have time to bubble collisions these are other bubbles of form and their bubbles which form which are not disconnected from our bubble but actually collide with it we'll come back to why such bubbles inevitably occur but heads in the census simply means counting these other bubbles it's a way of looking into the multiverse it's a way of looking into the landscape and asking what other kinds of bubbles can there be besides our alcohol anything which can be nucleated will be duplicated eventually as we'll say so the expectation is that anything on the landscape don't leave it in this manner and therefore can eventually be seen by an observer moving up toward the tip of the light from here or the tip horse or time like infinity they can be many census takers here yeah they all will rock to the right pivotal iPhone and we call the typical icon census bureau the place where the census takers comment in compare notes okay so the census taker is just some observer who looks back from progress later in later times and notice that at an early time he sees no businesses as time goes on he sees the earliest bubble collision the earliest nucleated second bubble as time goes on he sees more and more of the late time nucleated bubbles and in fact they look smaller and smaller on his sky that's the picture you should have as the census taker moves forward in time he can see back and see smaller and smaller structure on the sky the smaller and smaller structure corresponding to the later and later bubble relations that's the picture now there's going to be some reasons why this would be exceedingly hard to see in the real world but but in principle all of this can be seen let me summarise the geometry here the frw patch it's parameterised first of all Sigma remember that's asymptotic in space like infinity it can also be thought of as the intersection of the generators of the asymptotic light cone with the bulk of the geometry at this point though generators go into the bulk it is just the surface the two sphere at infinity and then in addition to the coordinates of Sigma we would also have the coordinates T plus which runs out and t minus which runs along the generators of the of the patch now let's think about the census taker for a minute here's the census taker again think of the backward light cone of the census taker what the census taker can see in this backward light cone that light cone is a surface of fixed T plus all right assuming the census taker is right at R equals 0 then as far as the census taker goes he is a surface of constant P plus or he looks back and sees a surface of constant P plus so we can identify the time of the census taker as it moves up here with P plus good that's interesting now think of a space like surface that the census take a look back and see some particular one it could be anyone they're all the same or left that is to say they all have the same geometry modulo the scale factor let's think about what the census that well let's first of all think about what those space like surface is alike those space like surfaces are hyperbolic flames I always include this picture in every seminar I ever get because I loved it so much I do believe that Esther made I made a bargain with the devil to be able to create an infinite number of them near the boundary here I can just see him working with his little pen but this is a picture of the hyperbolic plane this is two-dimensional of course we're talking about three dimensions and each angel and devil is of course are the same size intrinsic size proper size and there is a symmetry which moves you around from devil the devil that symmetry is of course translation symmetry or the analog of translation symmetry on the uniformly negatively curved surface it's the O 3 1 symmetry the symmetry which moves you around and slides you around and takes one devil to a neighboring so and so forth is exactly the O 3 one symmetry geometry has another name now not thought of as a as a sequence of different time slices but just at a particular time slice the negatively curved geometry like that also goes under the name of Euclidean anti-de sitter space Euclidean anti-de sitter space is exactly the same space as a space like surface of negatively curved frw let me just give you a quick review and a tiny tiny bit of information about the connection between anti-de sitter space and boundary quantum field theory this of course is the holographic principle coming into play the holographic principle says that the physics of anti-de sitter space the inferior the angels and devils are exactly equivalent to a conformal field theory that lives on the boundary so it's the holographic correspondence if you like how from the point of view of the field theory do we understand the radial direction the radial direction on the one hand can be mapped into size scale in the boundary quantum field theory the boundary quantum field theory is a conformal field theory if scale invariant if you have an object on the boundary you can make it smaller you can make it bigger the bigger the object the more it corresponds to something near the center the smaller it is the more it corresponds to something near the boundary another way of saying it is that the radial Direction corresponds the renormalization group flow sorry Laura no no objection from the line maybe is not here one good excellent now there's no real objection it's just that this correspondence is a fuzzy correspondence and it's fuzzy to within about 180s radius so um you wouldn't want to push it too hard at small distances but roughly speaking on a scale of the ABS radius which means about the size of one devil here this is a correct correspondence renormalization group flow motion in and out is renormalization group flow what I have here in mind for Kappa is of course the renormalization energy scale so the further you go out the smaller the distance scales of these angel angels and devils but also the higher the corresponding momentum scale in the dual conformal field theory so I want to remember that radial motion is renormalization group flow and the other thing I've written down here just for future reference is the form of a correlator of a scalar field of dimension Delta in the boundary conformal field theory well it's this is the structure that it has 1 minus cosine alpha cosine alpha is the angle or alpha is the angle between two points on the on the boundary or in the boundary conformal field theory represents the separation between points 1 minus cosine alpha goes to 0 when the points come together to the minus Delta that's the typical conformal correlate dictated or we become formal invariants come from I'm sorry I didn't even mention conformal invariants the important point is that the symmetry group of this space when it acts on the boundary generates conformal transformations ok so this is the typical form of conformal correlator in fact these factors here are really they're in correlation functions these are wave function renormalization constants wave function we normalization constants scale with the cutoff momentum to the power Delta they're really there in the correlation functions we usually strip them off and define the correlation function or define the fields in such a way is we've renormalized the field by multiplying by K to the Delta as we take the cutoff momentum larger and larger and then strip them off and throw them away and say that the conformal field theory correlators is this but they're really there even in the field theory we can also understand them in another way if R is log k then k is e to be R so this represents e to the minus Delta R what's going on is if we think of a correlators in the bulk and then imagine sliding them out to the boundary they fall like e to the power minus R Delta for each external line and in fact so the correspondence between bulk and boundary is very close wave function the normalizations just become the behavior of fields as you move toward the boundary ok now let's come back the cosmology this taker looks back and as he looks back at later in later time his back would like cone moves out moves out toward the boundaries of space they remember the t+ is a census taker time but we could draw that as follows or we can think of it as follows as the census taker time evolves his backward light cone expands out and moves out closer and closer to the boundary the point is that to the extent that there are interesting correlations on the sky interesting correlations on the sky first of all because of the symmetry the correlations and the asymptotic strive should be organized according to conformal representations why because they come formally symmetric due to the are due to the symmetry which manifests itself as conformal symmetry so first of all the observer will organize his measurements and then organizes observations according to conformal symmetry but as time goes on and this surface moves out and out and out it's quite clear that it's generating a renormalization group flow as time goes on the observer sees smaller and smaller structure on the sky and sees finer and finer detail on the sky and it is clearly generating some kind of renormalization group flow in some kind of structure which has conformal invariants now what is that structure on the sky is it a conformal field theory and incidentally since this surface is a space-like surface fully it's a space-like surface then this will have to be a 2-dimensional because the sky is two-dimensional Euclidean conformal field theory this is just a 2-dimensional spatial surface from the point of view of the causal structure of it well how do we find out what kind of structure it is the best way that I know is to start thinking about correlation functions of bulk fields on the boundary this is the same thing that we were doing in anti-de sitter space and the way to calculate is to start with the comb in the lucha bubble calculate correlation functions it's not so easy and they're making it sound easy it's rather hard but doable calculate correlation functions put the points into the flat space region analytically continue analytically continue from the comb and gallucci instant-on for the minkowski signature geometry and then slide the points back or push the points back through the boundary this is very similar to what we do in anti-de sitter space except there's an extra dimension there's a time dimension in addition for the filadyne mention in the surface question is there a dual Euclidean two-dimensional conformal field theory on Sigma and if there is how do we understand the extra dimension of time alright I'm going to do boy do I really want to fill through this yes I'm going to go through it you're your hostage to me now because the Oliv doors just been laughing you cannot get out I'm gonna tell you what the correlation lock the door please would you mind walking in the door how much time am I gonna Buddy my got it let me tell you what's here these are calculations of the of the correlation functions for tensor and scalar fields tensor meaning the gravitational fluctuations scalar meaning minimally coupled scalar minimally coupled scalar massless I'm going to just briefly tell you there are two kinds of contributions to the correlation function and I have names for them I used to call them proactive and reactive with stupid names my wife made them up knowing nothing whatever about physics I just have to give me two words and she said proactive in color but I realized later that I'm really talking about renormalization group covariant and renormalization group invariant operators are in the invariant correlation functions and I'll tell you what that means as we go along but in any case here's what follows first of all you can see the structure of these correlation functions have some three factors in front of them that depend on the x and radial distances the three pluses and the minuses of the external points alright when you pull them back to the surface Sigma P plus and P minus asymptotically go to some values all right but each one of them each term in the expansion is a conformal field theory correlator and they're discrete that's a surprise that they're discreet not obvious if they should be a discreet collection of them the discreet they have integer dimension and they begin as I mentioned to and notice that this term has a trivial dependence on T plus in other words as you move out for the boundary every term in it has exactly the same fee plus term endures behavior but the interesting dependence is on T - and that contains the dimension of a field and the form of it there's a constant times e for the something involving delta times t minus as you move along here times 1 minus cosine alpha Philadelphia so we see a collection of conformal correlators but I want the main thing about it is that it depends on P - in a certain way then there's another collection of terms where they came from that is not so important right now the structure is important and the other term which I call the renormalization group invariant depend only on t + don't depend on T - at all in the case of the tensor correlations there's a term here how do we understand that term that term can be understood as zero dimension as a zero dimension operator logarithmic divergence is instead of power law divergences or what you expect for dimension zero operators so first of all is the dimension zero operator which I will identify in a little while as a level field from the boundary on the asymptotic boundary and then there's a collection of things which just depend on feet plus with the prefactor Z to the minus Delta P plus times the same kind of conformal Hanalei deserve fear here seem to be two kinds of objects and the interesting question is what are those two kinds of Konnor things correspond to what are they from the point of view of the of the potential hypothetical boundary field theory what are these two things to come back for a minute what does this piece tell you this piece is only there for the tensor correlator for the tensor correlator is this zero dimension piece and I called it Lea ville if you look at it this term is pure gauge don't worry about it it's just pure gauge if it's it's trivial I take it from me believe me this is the interesting piece here and it doesn't depend on radial distance it's just fluctuations in the geometry which extend out to infinity in other words it is not like anti-de sitter space where the fluctuations in geometry are frozen at infinity and go to zero but rather there are fluctuations in the geometry which extend out to infinity with a quick constant coefficients which means in effect that the geometry at infinity asymptotic geometry of the surface of infinity is not round it's got a geometric texture to it and that geometric texture is dynamical in the same sense that all the other fields of dynamical we frozen with time no time dependence in it but it is has some statistical distribution roughly speaking what it says is that the asymptotic geometry is lumpy lumpy and has multiple moments of all kinds why is this this is the effect of the asymptotic warmness of the non asymptotic coldness of cosmology that's and that's the difference between anti-de sitter space that the asymptotic behavior is not frozen in the same way what does it manifest itself in it manifests itself in a level field liova field are just we're gonna go through what little fields are and how how they work you know it's a lot a few minutes but let me just for the experts on it just point out where another way of thinking about this little field the s squared this is the area element of a two sphere namely the two sphere which is represented by this green line the Green Line is not at the boundary it's at some R and at some time in general that looked like a of T squared so I'm cinch squared R times D - Omega squared or a of T squared times e to the 2 R e to the 2 R because the Cinch asymptotically is just e to the 2 R I'm going to give this a name I'm going to call this the reference metric this piece over here and that would be there incidentally in the anti-de sitter space the new thing is this time dependence here well if the geometry is asymptotically warm that means that there are not well-defined frozen clocks at infinity that keep track of time in a way which is appropriate for example for an ABN description time everything fluctuates out infinity and it doesn't make any good sense to say time you have to think of time as a local thing the time over here the time over there and so forth or another way of saying it is the formalism should be invariant under transformations on their shifts though I'm only talking pretty much about shifts far away now asymptotically because that's where I'm concentrating P goes to T plus some F of Omega 2 the formalism should be invariant on that under that because there is no preferred time in asymptotically warm geometry that means that this the S squared is really going to have instead of just the reference metric times e to the global time it's going to have something which depends typically on position on on the sky e to the U Omega of Omega 2 this is what is called a little field a metric which depends on a reference metric times a field which varies over the over the sphere over the geometry now is this dynamical yes it is dynamical in order to make the formalism gauge invariant you have to integrate over these shift functions or these laughs I guess this is a lapse function you have to integrate over them very similar to what you would do in the wheelers the wit formalism and this e to the Omega - really does become a dynamical field it's a little field for experts it happens to be a time likely oval field which means it's kinetic term is negative we can come by or you come back to there why that's so so the main point in the main lesson now is that in addition to the degrees of freedom that you would have in a anti-de sitter space you have additional degrees of freedom associated with the geometry of the boundary which don't go to 0 and they correspond to 0 dimension fields which would not be present in anti-de sitter space but otherwise it's very similar ok so let me go on and tell you just a little bit about how the renormalization group flow works I will not get to the end of the seminar I never get to the end of my seminars but let me tell you a little bit about how the renormalization group of level theories work and how it's connected to the origin of time and to the space-time that it's trying to describe really is a trick for summing over for summing over surfaces all the people who study two-dimensional quantum gravity are extremely familiar with it and one of the ways of summing over surfaces is to triangulate them with fishnet diagrams are you triangulate them and instead of summing over the metric you simply sum over the structure the triangulation itself everybody who does quantum gravity Phi Phi Phi angulation will recognize what I'm talking about and we can if we can think of this fishnet as actually defining a true metric we want the sum over it well we're trying to do something which is beyond the normal rules of quantum field theory we're trying to do a path integral over geometries offhand we don't really know how to do that and so the experts who do this kind of thing and try to do it by using standard quantum field theory do the following trick they introduce a reference ladder so a reference metric you can always think of a metric as a kind of lattice they introduce a reference metric the only rule being that the lattice spacing on the metric car on the reference metric should be a lot larger than the math and the lattice spacing of the other true metric and the reference metric is kept kept absolutely fixed it corresponds to a lattice for example for definite lattice on the sphere of the sky we're not going to vary it when it's it's arbitrary but fixed arbitrary we fixed a reference metric and then we integrate over all the degrees of freedom as this as this fishnet moves around incidentally the fishnet can also have of its vertices are the kinds of degrees of freedom icing degrees of freedom all kinds of things we integrate over them and define effective fields either at the vertices or in the triangles it doesn't matter very much we define effective renormalized averaged fields the the condensed matter physicists would call them Bloch spin fields or whatever we like in on this fixed lattice integrate over them and that defines a quantum field theory on the fixed flattest that's the idea of liberal field that's what liberal theory does now the definition of the level field is simply the relationship between the true metric and the reference metric whatever reference metric you pick the true metric is related by e to the U times the reference my v let me just go back a step and point out the similar already with this formula here and also remind you that this U is simply local time a local time near the boundary so Leoville does have a structural similarity to what we're doing but what I want to talk about for just a very short brief time is the renormalization group structure of a legal theory well first let me remind you about renormalization group structure in ordinary field theory we normalize this this is what I call the Wilson line the Wilson line simply means the line of scales starting at the infrared and the infrared could correspond in QCD it could correspond to the confinement scale in our problem it corresponds to the size of the sphere that we're doing our field theory this is a coordinate size of the sphere in our problem it's an infinite axis if it's a continuum field theory but we pick a point which we call either the renormalization point I'm going to call the reference point again it can't it's just a reference lattice if you like in the field theory and we integrate out all the degrees of freedom on scales shorter than the reference scale that defines for us an effective action at reference scale R that's basic that's an ax nutshell that's renormalization rope okay minimization group refers to the variation of this L of R as you move this point around what's the difference with Leoville theory well little Theory you actually have two scales you have this fishnet scale it's a local scale it varies from place to place but you can think of it as the bare lattice spacing in the theory it is to be integrated over it's not something which you choose its to be integrated over but let's suppose that it fluctuates about some mean so put it out here that's the fishnet scale on one hand and then there's the reference lattice scale over here so there were two degrees of freedom the Louisville field is the ratio of these two scales and logarithmically logarithmically are the liberal field the liberal field is simply the distance from here to here okay but we also identified the lethal field with local time so here you see the origin of a new time scale which did not appear here this could have been a BSC F P and this our variable is just the R coordinate of the ABS the radial coordinate and it is the renormalization group scale here we have another scale the other scale is the distance logarithmically between the arbitrary but definite reference scale and the true short distance ultraviolet scale of the theory which as I said we do integrate over notice in both well in this case here in particular that we would tend to a continuum limit by going to large team a continuum limit remains that we take the lattice spacing here smaller and smaller and to get to that that corresponds the increasing time so very late times correspond to the continuum limit of this little theory I'm going to assume that the continuum limit is at a fixed point just for fun it doesn't have to be at a fixed point that is at a fixed point of the renormalization group what that means is that you integrate out as T gets larger and larger you integrate out more and more degrees of freedom and eventually run through a fixed point that's my assumption that will run to a fixed point of the renormalization group so fixed point physics and continuum physics would correspond to very late time physics and that's a theme throughout here that the end point of a renormalization group flow with a fixed point corresponds to asymptotic relate times cognise that people are going to have trouble yes but you have to see it a few times before you get it in my own opinion it is rather important so let's let me continue now let me explain to you these two objects that appear in the correlation function see you know what I don't I don't know whether to stop with people out of here what should we do it's an hour gone by and not finished and I can stop right here and mmm yeah continue for those who want it we can do all we can yeah the final product the five-minute summary is that the renormalization group flow corresponds to the observations of the census taker as time gets later and later looking out further and further into the sky and quantum field theory is the organizing principle to organize those those observations that's the bottom line and much about the structure of the sky now remember we're talking about zero cosmological constants caveats here but much about the structure a very cool sky way lately on the surface of last scattering that you can only see by gravitational waves much about the structure of the sky is organized and determined by the dimensions of operators in this conformal field theory the way in particular the time evolution that the consensus paper would see of the sky is determined by the dimensions of operators and so I don't know if we can I'm happy to continue I'm also happy to stop

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Keywords: Leonard Susskind (Academic), Eternal Inflation, Physics (Field Of Study), De Sitter Space, Star, Voyager, Sci, anti de sitter space, flat space, science, Physicist (Profession), Cosmology (Field Of Study), Willem De Sitter, Max Planck (Academic), nucleation, bubble nucleation, Lecture (Type Of Public Presentation), Colloquium (Business Operation)

Id: pdZf8cCBOsA

Length: 58min 20sec (3500 seconds)

Published: Sun Oct 25 2015