Cosmology | Lecture 7

this program is brought to you by stanford university i want to come tonight to the idea of inflation inflation is an important idea in cosmology maybe one of the most important and uh sort of at the root of much that we know much that we suspect about cosmology but before i do let me remind you about what the presence of a cosmological constant does in einstein's equations the cosmological constant i'll remind you is just a term in the energy which doesn't dilute as the universe expands an energy density which does not dilute so it's just a term in einstein's equations einstein's equations are the same as the friedman robertson walker maker equations a dot over a squared is equal to the energy density and i'm going to take the case of flat space although we may want to modify that later the case in which space itself is flat not space time but space and in that case what goes here is just eight pi over three times newton's constant times the energy density and in general the energy density may dilute the energy density or mass density we discussed various cases there was the case of matter dominated where rho was just the mass energy of a collection of particles that are expanding because it's expanding the energy density decreases and in that case rho goes like 1 over a cubed we studied the case where rho was radiation energy that's what dominates in the very early universe it was 1 over 8 to the 4th and we also talked about vacuum energy and vacuum energy rho is just constant so we can just call that rho naught or we can call the whole thing on the right hand side uh lambda or something proportional to lambda there's some definition of lambda the cosmological constant which includes i forget how many eights and pies and so forth but this whole right hand side would be a constant then all right let's suppose this is a constant let's call this constant let's just give it a name h squared why am i and h is a constant it does not change with time that's the nature of vacuum energy the nature of vacuum energy is the right hand side doesn't change of course the re the reason i'm calling it h squared instead of just h is because the left hand side is a square and this will uh have the nice properties when i take the square root it will say that a dot over a is just equal to the constant h where h is the square root of the vacuum energy times g times 8 pi over 3. that's that's square root of 8 pi g over three times the vacuum energy rho naught rho naught just means vacuum energy so if you know the vacuum energy then you know h as i emphasize uh h is a constant right and then a dot over a is just equal to that constant this is a special cosmology that has nothing in it but vacuum energy now remember also that a dot over a is also the hubble constant so for this very special case where there is nothing but vacuum energy nothing but vacuum energy that is a special case uh when there's nothing but vacuum energy the hubble constant is truly constant it doesn't change with time if the hubble constant doesn't change with time what does that say about a well we can write it as a dot which is the a by dt is equal to this constant hubble constant times a and the solution to that equation is an exponential the rate of change of the scale factor is proportional to the scale factor with a constant of proportionality just equal to h and the solution to this is a is equal to some constant it doesn't matter we can just ignore what the constant is and write e to the ht in other words the scale factor or the distance between distant galaxies unbound galaxies galaxies which don't have enough gravity to between them to keep them from receding the distance grows exponentially that space time that space time which is exponentially expanding in that manner is called the sitter space it's just a very simple solution of einstein's equations with a positive cosmological constant incidentally i've assumed that the vacuum energy here is positive right could it be negative yeah it could be negative but in fact let's take the case where it's positive the vacuum energy density is positive then the then this is the solution and when i say it's the solution i mean to say that the geometry the tau squared is equal to dt squared minus a squared which is minus e to the 2h t that's a squared times the x squared and the x squared means the x squared plus the y squared plus dz squared how could it be negative do you have a positive positive quantity on the left-hand side yeah yeah yes you're you're right it it can't be negative and space be flat the um it can be negative if space is not flat for example um there is the curvature term here plus or minus one over a squared uh but you're right the whole thing here has to be positive in order that the left-hand side be positive uh but this can be negative and this be positive and something else happened but but let's not belabor that because we're going to take it to be positive in any case the vacuum energy to be positive einstein put his cosmological constant in to make sure that the universe wasn't expanding is that how he did it is he just well what he did was to say we know that there's ordinary energy in the universe so let's put in plus some constant m over a cubed and then thought about the possibility of cancellation between this and this also he put rho naught equal to minus m over a cubed okay it was a mis it was a misstep it didn't make sense right but that's that's why he introduced it in the first place okay in any case in any case this geometry this geometry which exponentially expands distance between any two points exponentially expands it has a constant hubble parameter is called the sitter space discovered by the dutch astronomer wilhelm de sitter very shortly after einstein invented his theory long before it was known that the universe was expanding and it's an important space time in cosmology it's important for two distinct purposes one of them is the explanation of the currently accelerated universe acceleration what does acceleration mean it just means uh that the second time derivative of a is positive let's go back to this simple this this case over here this of course would be called an unaccelerated universe because the second time the derivative of a is just playing zero this is accelerated because the second time derivative of a uh is positive and in fact growing uh with uh with time all right so that's the accelerated universe it's an observed fact today today this is a correct description of our universe not quite and not quite because there is some additional energy besides just the vacuum energy so let me just remind you quickly what we know from observations we know that the scale factor in the past was this usual t to the two thirds that's the matter dominated universe and then at some time of order a few billion years ago somewhere is more or less at the halfway point between now and uh and the big bang it uh it began to exponentially increase or it began to increase more rapidly now t to the two thirds doesn't look like that does it yeah curvature is wrong t to the two thirds look like that convexity is wrong right and then at some point it it did start to look like that and we're somewheres over here so this is an observation this is not something which is speculation and there's enough of this curve here that's been measured that it does fit neatly on to the exponential it itself of course is not quite an exponential because it's a transitory behavior but it appears to all uh all observers tend to agree it looks like it's entering into an exponential phase which is another way of saying that the vacuum energy is bigger than the other energies roughly by a factor of two today but this is getting smaller and smaller with time and this is not getting smaller and smaller with time so that's a current that's our current understanding of the universe today it's exponentially growing it's the center space and the hubble constant which is not exactly constant today because it's not exactly exponential but is tending to an exponential all right that's today uh it is also worth discussing the idea of a horizon i think we've done this before but let's do it again it's an important idea at some relative coordinate spacing let's call it delta x or somewhere some let's not coordinate spacing at some distance some actual proper distance using hubble's law we can calculate the velocity as a function of that distance and at some distance it becomes equal to the speed of light all right remember that distance times hubble is equal to velocity and so if we want the velocity to be the speed of light then the distance that we have to go out to is equal to the speed of light divided by that hubble constant the hubble constant being the square root of a vacuum energy density the smaller the vacuum energy density the smaller h the bigger the distance to that place where things are receding away from us with the speed of light that place of course is called the horizon and if you like it's a sphere around us at a distance given by c over h numerically it's about 10 or 12 or 15 billion light years which accidentally happens to be about the same as the age of the universe now whether that's an accident or not is a matter of very intense argument but they're two different quantities one is the age of the universe in other words the time where is it i threw away my graph but there it is universe started and then this and we're over here okay so as it happens this distance scale apart from a factor of the speed of light is about the same as the age of the universe so the distance is about 10 or 12 billion light years away and at that distance as i said this yeah isn't it hubble isn't the tangent line to the uh at any point if it happens to intersect the origin then those two quantities will uh coincidentally be the same in other words distances that of course would be exactly true for a of t equals t right right yeah okay so at the moment it is a bit of a mystery why the vacuum energy happens to be such okay that the distance to the horizon or converted to a time by means of the speed of light why the distance to the horizon is about the same as the distance uh to the surface of the surface of last scattering but if you like to the age of the universe not knowing exactly why that's true coincidence as far as we know well it's not remaining the same either the horizon is a change the the hubble constant is remaining the same of course the age of the universe is not remaining the same right right so as far so it sounds like it's a coincidence of just us be being here at the time that we're here right let's tell you let's take it to be just a coincidence now is it a coincidence is it a coincidence that the darwinian time scale for evolution happens to be the same as the time scale as obtained from the vacuum energy no that's clearly something which we have to explain someday in the in the center space is that assuming that there's no matter or and no no radiation yeah okay that one happens to this we have a situation where the so i guess there's a form of energy this fact can you say something about this documentary because i'm pretty confused about what its source is or what it is i mean you would think that if you didn't have any matter or radiation you'd get nothing i mean naively right so for that we have to understand why quantum mechanics gives energy to the ground state of systems the vacuum is the ground state of let's say quantum field theory ground state means the state of lowest energy now in the vacuum it's possible to have oscillations of electric and magnetic fields and so forth the oscillations behave like ordinary oscillations and ordinary oscillations have a ground state energy the ground state energy is not zero and the reason that it's not zero is because of the heisenberg uncertainty principle we're going off track but let's answer the question anyway if we have a harmonic oscillator what's the potential of a harmonic oscillator the energy of it is proportional to the momentum square that's the kinetic energy i'm not going to put in numerical factors plus the distance squared that you stretch the spring so to speak all right there's usually a factor of spring constant here and a factor of one over twice the mass here but just leave it like this this is good enough for us p squared plus x squared now classically the ground state of the harmonic oscillator simply means the configuration in which the spring is at its equilibrium point not vibrating not stretched to sitting at its equilibrium point x equals zero and because the velocity of it is also equal to zero at the equilibrium point p is equal to zero and the energy is equal to zero p squared plus x squared both of these terms are equal to zero the heisenberg principle does not allow there to be a state in which both x and p are simultaneously knowable in the language of quantum mechanics diagonalizable and so there's a necessary fluctuation if x were literally right at the center here then p would have to have an infinite fluctuation if p were at the center in other words if the momentum was exactly equal to zero then x would have to have an infinite uncertainty and so there is no state of the system in which both p and x are exactly known to be equal to 0 they both fluctuate but the sum of p squared plus x squared doesn't necessarily have to fluctuate but it's got to be positive since both p and x cannot simultaneously be zero the vacuum or the ground state energy of a harmonic oscillator is not zero now what is it what is the ground state energy of a harmonic oscillator one-half h-bar omega where omega is the frequency of the oscillator now the universe is full of potential harmonic oscillators full of harmonic oscillators they're the oscillations of the electromagnetic field there's in fact an infinite number of them of low frequency high frequency and a large number of such oscillations not just the electromagnetic field but every field and every field has a ground state energy it's the energy stored in that field due to zero point oscillations every every field behaves like an oscillator every field has zero point energy and it's those zero point energies which are one explanation of the vacuum energy the real puzzle is why it's so small it is very small numerically very small but uh that is not for tonight let's just recognize that it exists as the universe expands it doesn't dilute it's just a constant and experimentally it really is or observationally it really does seem to be there with a particular numerical constant which happens to be extremely small measured in natural units i have an idea why isn't that just the the last scattering baseline energy i don't know what that means i just mean that there's there's always a three degree it's not the three degree radiation that's radiation that energy decreases with time because the photons dilute and furthermore each photon decreases its energy it's not the three degree it's the oscillations that are there when you remove all the for all the real photons it's the virtual photons or the just the zero point oscillation that uh that is necessarily present of course we're not now talking about a particle on the end of a spring we're talking about the fluctuations of the electromagnetic field in fact you know what these two things would be for the electromagnetic field which uh which can't for which there's an uncertainty principle well isn't this like sources electric and magnetic fields the energy of an electromagnetic field is e squared plus b squared with e being like momentum and b squared and there's an uncertainty principle between electric and magnetic fields which is very similar to the uncertainty relation between velocity or momentum and position okay so they can't both simultaneously be zero because of an uncertainty relation between them and the result is that even when you remove as much energy as is possible to remove from the field there's still this residual zero point energy that's what constitutes or at least that's what's believed to be the origin of this i'm starting a tough time understanding if you remove matter and you remove radiation what causes the electric fields like what's the perturbation and what i can't answer what causes it i can tell you that the uncertainty principle requires it to be there but we're making the assumption there is no electric field there is no mass i thought you did i say there's no electric field so sitter space has only the uh the dark energy okay it has no real photons it has only the zero point energy okay you can have an electric field without real pulling it just doesn't have any charges it's there anyway the field fluctuates anyway it doesn't need charges right all right yeah could you go over that point about the age of the universe being equal to the uh inverse hubble constant yeah okay let's take a look i know it is equal to inverse total constant but it's also equal to the distance to the surface the last scattering oh that's that's an approximation that's the distance to the surface of last scattering but uh um isn't that just a mathematical truism just because of the equations it's just yeah it's not an experimental effect um almost almost yeah but not that h not that h is approximately the age of the universe no clearly it does not have to be in this deciduous space it's simply not true h just never changes the age of the universe does change it's exactly true it's only exactly true for this scale factor over here let's see why all right let's let's take this case a of t grows like t then what is h h is equal to a dot over a what is a dot a dot is 1 and t and a is t so this is just equal to 1 over t and it's clear that the hubble constant it's not constant but the hubble parameter is just one over the time the time from the big bang any power law well it's not quite true take any power law here then it becomes then a dot is equal to p t to the p minus one and then divide that by a that means dividing it by t to the p and the answer is p over t so for example if p is two-thirds then this would be two-thirds over t and it would not quite be the case that the hubble constant was one over time but it would be one over time with a factor of two-thirds in front of it yeah but i'm assuming there's other constants we're not including anyway all right that's right three so there will be three halves in front of it eight should be three-halves one over t oh did i write the uh one over p so no that's right two thirds is right but h h is right okay yeah two-thirds is right that's h left-hand side is h for the d sitter universe it's infinite wait okay wait h is equal to 2 2 over 3 t where t is the age of the universe at any given time okay now let's come to the descender case the decider case is not t to the p it is e it's exponential e to the ht let's not call it h okay let's just call it e to the constant gamma t all right a is e to the gamma t what is a dot incidentally i could put a constant in front of it it wouldn't make any difference let's put the constant in front of it what is a dot a dot is c gamma e to the gamma t right just differentiated e to the gamma t now divide it by that's a dot divided by a which is just c that cancels c and it cancels e to the gamma t so we find out that the hubble constant now is truly constant and it's just this gamma which appears here okay this is the unique case in which the hubble constant is constant it's the only case where it's constant uh once we know that the hub that that a dot over a let's go back a dot over a is equal to the square root of 8 pi g over 3 times rho this is the square root of the frw equation all right so the hubble constant is just the square root of 8 pi g over 3 times the vacuum energy that's h right so there's a definite connection between this vacuum energy on the one hand and the hubble rate of expansion we call it sometimes the rate of excel the hubble rate of expansion it's the thing that goes in here it tells us in this case 1 over h is not the age of the universe what is it it's the time constant it's a time that it takes the universe to double and not double in size but multiply by e yeah the time that it takes for the universe to double i said double again let me use double but i really mean multiply by e it's the time constant for the universe to double in size and what is that that is the inverse of this h and it's about 10 billion years okay so every 10 billion years we can expect the universe will double in size roughly roughly speaking that's an approximation this vacuum energy density is constant right yeah it's constant well yes this of course is an experimental question okay so if the universe is expanding so that applies to me that the energy the total energy vacuum energy is increasing where is it coming from it's coming from the other side of the equation this minus this is equal to zero this is one form of energy this is another form of energy this is a kind of kinetic energy of expansion it's kind of kinetic energy of expansion uh both terms appear in the expression for the energy and in general relativity and it's conserved because it's equal to zero so it's by so this energy is coming from here that comes from einstein's field equations if you apply einstein if you apply the ideas of hamiltonians and energy to einstein's field equations we talked about all that kinetic energy at the beginning yes right so is that basically being transferred yeah it's a transfer of kinetic and potential energy when we talk about energy being conserved or entropy increasing are we talking entropy or energy either one okay are we talking about that within the cosmic horizon or do we mean the cosmic horizon is fixed in size it doesn't change with time that's the same statement that the hubble constant doesn't change with time the energy within the cosmic horizon stays fixed with time the vacuum energy the vacuum energy is just the volume of this times the vacuum energy density the vacuum energy density which is rho naught let's let's just let's work it out um okay so that's this diameter here which is what is it uh c divided by square root of 8 pi g over 3 times the square root of rho naught in the denominator that's the distance now i want to what i want to do with it i want to cube it in order to find the volume cubed yeah four thirds four thirds pi okay and then multiply that by the vacuum energy density and the vacuum energy density is rho naught itself there's some amount of energy in there but it doesn't change with time it doesn't change with time the amount within the cosmic horizon so the portion that we can see the portion that we can ever see uh that energy doesn't change with time if it's the sitter space right if it's the center space right so you know standing here from our vantage point and looking out and looking at all the vacuum energy that's out there no it doesn't change with time the portion that we can see okay good so that's that's the basic idea of a cosmic horizon things can pass through the cosmic horizon in the same sense that they can pass through a black hole horizon and i won't go into that in any depth now but uh once they do they're out of contact with us and they're gone so if it's not at the space does that mean that energy flows beside the customer to energy within the cost of horizon it might well energy is energy is a loaded term exactly what do you mean by the energy in general relativity in general relativity the concept of energy is a little bit curious because it contains this gravitational component as well as ordinary energy this is the gravitational component of the energy here for this particularly simple kind of uh geometry yeah let's uh let's move on all right now the same the same mechanism appears to have happened in the remote past but instead of the time constant being about 10 billion years it was about 10 to the minus 32 seconds or perhaps that that fast where does this come from well the origin of the question this is inflation this is the idea of inflation the universe and the remote past exponentially expanded now when i say this happened of course to some extent this is conjectural but the conjecture has passed a number of observational tests so when i say something has happened you can feel free to put a little bit of a question mark did it really happen or or am i guessing okay so i will tell you what's known and what the empirical evidence is but let me just shorten my sentences by saying something happened it's all right it happened that in the remote past before anything that we can observe in other words out beyond the surface of last scattering or earlier than the time when the universe became transparent universe was exponentially expanding now why did that idea gain any traction and where did it come from well the basic place that it came from was the flatness of the universe to make a long story short spatially the space slices of the universe are rather flat flat meaning we don't seem to live in a curved universe which is either positively curved or negatively curved we seem to live in a very flat universe in fact not only a flat universe but a rather homogeneous universe on large scales bigger than superclusters of galaxies in particular on the largest scales the universe is very flat and homogeneous and smooth how did it get to be that way and why is it that way the early ideas of the big bang were that the universe started just in some random state it could have started with some very complex geometry it didn't have to be flat and it didn't have to be homogeneous we don't really have a theory of how it began in the very very beginning but let's suppose it began like a shriveled up raisin or prune with all sorts of wiggles and texture to it right why what is where did all those wiggles and texture go where did it disappear to now in fact we know here's something we know we know at the time of the surface of last scattering in other words at what we ordinarily think of as the big bang the beginning the beginning as far as we can see back already at that time the universe was very flat and smooth so it's not that it flattened itself out and stretched itself out between the big bang and now big bang i mean looking back to the surface of less scattering the surface of less scattering itself is very smooth which indicates that at the time when the universe was as hot as the surface of the sun it was already very smooth so something had smoothed it out now you might say why do you need something to smooth it out just postulate that it started out smooth okay you can do that uh and but in fact it wasn't exactly smooth we'll come to the deviations from smoothness but the question was asked why is it that the universe started so very smooth why is it that the density in one place is about the same as the density in a very very different place in particular we can imagine places which are so far apart that light we can we can see them both all right we can see them but we see something way out there and something way out there but we know that light did not have time to get from one to the other so there was no way that a smoothing process could have happened on such large scales and what is it that made the universe smooth and flat on those scales well the hypothesis is that the big that what we ordinarily call the big bang that there was a prehistory to it and during the prehistory of it the universe exponentially expanded by an enormous amount and got itself stretched out to be almost completely flat likely inflation of a balloon i i like to think of it that way you start with a completely deflated balloon and the completely deflated balloon looks uh looks like a uh um you know what a completely deflated balloon looks like okay it has all sorts of uh wrinkles a wrinkle a wrinkly balloon a really wrinkly balloon and now you start blowing it up and after it's expanded a certain number of times it gets pretty homogeneous it gets pretty smooth okay so if there was and this prehistory would have had to be before the surface of last scattering because it's known it was already very smooth at that time right what was the hypothesis the hypothesis was called inflation due to alan guth in the era in the early 80s around 1980 that the universe underwent at that very early time a period of exponential inflation exponential growth in other words that for a period it behaved like the sitter space are we assuming equilibrium before inflation no no no no whatever inflation does it stretches things out so much that you lose memory of what the structure might have been like before inflation started it just takes whatever was there and stretches it out so much that it just leaves it in this very very homogeneous configuration there was no previous homogeneity we don't know we don't know one of the good thing about inflation is it erases all the initial conditions and so you don't have to know what the initial conditions is because you don't have to know what the balloon looked like in the beginning because it gets stretched out the bad thing about inflation is it erases all the information about how it started i don't know i mean if you had a blotch on the on a raisin and you blew it up then you would still have a blotch now you're blowing it up to something very much bigger than the size of the known universe so imagine there was a blotch on the raisin and the raisin got to be 10 to the 10 to the 10 to the 10 times bigger than the observed universe exponentially remember the idea was it was exponentially growing so it got to be 10 to the 10 to the 10 to the 10 to 10 times bigger than the observable universe so it's just as if the surface becomes transparent from previously okay or something it's not transparent it just it just gets stretched out it just gets stretched out so that that blot or that blob that little bit of inhomogeneity got stretched out it's still there but it's there on a scale much much bigger than we can see okay but you have to assume that it wasn't sort of a fractal to start right because in that case you wouldn't even you know yeah you had to assume that uh that there was smoothness on some terribly tiny scale but if the universe expanded enough if it inflated enough then if you start on any scale with some fluctuation it will eventually stretch that fluctuation out that's known as inflation and the hypothesis is that in the very early universe that basically exactly the same kind of thing happened that is happening today except with a hubble constant at that time which was millions and millions of times larger larger yes larger in other words with a vacuum energy which was very much larger than the vacuum energy that we see today okay now that's a curious idea it's a crazy idea why was the vacuum energy different then than it is now can we even call it the vacuum energy if it was if it had to do with something which is different than the vacuum today and what's the basic idea all right so the basic idea goes something like this now we do have to talk i'm going to tell you what the idea is and then we'll come back at some point i hope and discuss what the empirical evidence for this idea at first it was just almost a throwaway idea maybe something like this happened and as time went on observation got better and better to the point where this picture has been pretty well confirmed by now that doesn't mean it's absolutely got to be right it means that it's the best candidate for our understanding of what happened all right to understand you have to you have to have the idea of a scalar field a scalar field is a field just like maxwell's field just like electric and magnetic field except instead of being a vector at every point in space the electric and magnetic fields are vectors they have direction at every point in space it's just a scalar no sense of directionality and let's call that field let's give it a name let's call it phi is it any of the fields that we see in nature today is it identified is it are its quanta identified with any of the known particles definitely not definitely not it is not identified with any observed fields that we know about in in physics and its quanta are not identified with any known particles so it's a hypothetical field which exists in fill space same way as any other field uh and it has an energy it has an energy associated with it the energy that's associated with it is a kind of potential energy and a potential energy that scalar fields can have and it's a potential energy v which the v is standard terminology for a potential energy it doesn't when i say it's a potential energy i mean it doesn't have to do with the time derivative of phi of course there's energy in a field if it's oscillating if it's fluctuating but there also can be energy in a field just because the field is displaced away from zero value we'll find now this this for the moment let's completely forget about quantum mechanics quantum mechanics is not important to the discussion right now and it's some potential energy called vfi vfi is some function of phi let's just draw some picture of it here's some picture of it any function whatever function you like you can put in here and uh of course you get a different theory out no matter what function you put in here but imagine some function of phi then if phi is one value or another value or another value or another value the field energy and it's a kind of vacuum energy it's a kind of energy that's there not really in the vacuum but there simply by virtue of having some space in which there is a field which takes on a particular value it's very similar to vacuum energy via phi but it can vary as a question about that drawing is that what's the act the horizontal axis is sorry phi and the vertical axis really okay right all right now you have to you have to you're buying a whole uh set of ideas here which none of which are obvious first of all that there can exist scalar fields in nature this is not obvious that they have potential energy well the mathematics of field theory suggests that they that they can and do have potential energy and the potential energy can vary from point to point so different values of the field can have different energies right but one also has to take it as a matter of uh you have to take it as a matter of faith i take it as a matter of known mathematics that vfi if phi is not changing for example if it just has some value over here is a kind of vacuum energy it's a kind of vacuum energy which doesn't dilute that's the main property of it it doesn't dilute this part of the energy of a field doesn't dilute yeah the the if you drew a picture of space then would fly be constant over the space it may or may not be constant yeah it could have different values in different places that's right let's for the moment suppose that it was the same everywheres let's take that case for the moment all right we take that case for the moment and we say what would the world be like let's say what would what also phi itself is a function of x y z and t in principle it could be a function of x y z and t let's take the case for the moment where it's just constant for whatever reason at some value of phi then in effect the world has a vacuum energy which is just v at that value of phi that's the way scalar field energies work they behave exactly like vacuum energy in particular they don't dilute so then if that were the case we would simply say that the vacuum energy is replaced by v of phi where phi is the value that the field happens to have it might be over here might be over here as long as it's not changing with space or time it would just be a constant phi being constant in space and then we would go back to all the equations for the sitter space or all the equations for the expansion of the universe and every place we saw rho naught we would stick v of phi in particular the universe would expand with a hubble constant which would be equal to the square root of 8 pi over 3 g and instead of rho naught i would write v of phi now what happens if v of phi if i varies from place to place supposing over here it's a different value than it is over here or different value than it is over here well first let's go back to the case where it's not varying what's happening where it's not varying the region of space over which it's not varying is expanding exponentially like e to the ht what happens if it varies from place to place then in different places it's expanding expanding with different time constants but stretching exponentially by an amount that depends on v at every place so if v is varying or phi is varying from place to place you would have exponential expansion everywhere but a different time constant in each place right but if the universe expands enough if it inflates enough if it stretches enough and you're inside there someplace and you can only see out to your horizon eventually the stretching is so much that your entire environment your entire environment has been stretched out to the point where the field within your region has become homogeneous has become constant so it's very much like this balloon the balloon could be painted with some color which varies from place to place red over here blue over here purple in between and then you expand it out inflate it out by many many orders of magnitude and somebody at the center or somebody at some point who only can see so far sees a very homogeneous color all right same thing with this inflating universe v might vary from place to place but if it does vary from place to place it will get stretched out in such a way that that it will look for practical purposes as if it were very constant now it would worry me though if uh very let's say you know very proportional to something in other words it's not what you seem to have drawn is a situation where fear is constant and patches and it seems to me like it could be it doesn't have to be constant just slowly varying slowly slowly slowly varying on what feet on what scale well it doesn't matter much because whatever scale it's slowly varying on eventually that scale will get stretched out now you could imagine maybe it was so bad to begin with that it would never stretch out you could imagine that but apparently that's not the way it was and that we judge because the universe is today rather homogeneous right so let me draw for you then the way experiment various combinations of observations suggests this via fi to be oh ins yeah all right incidentally if you have a potential energy function which looks like that it could be the potential energy instead of for a field it could be for a coordinate of some kind what happens if you start the coordinate over here what happens if you start a particle in a potential energy and you start over here you roll down now uh let's suppose you start up here you roll down you roll over the hill you roll over the hill and you eventually go somewhere else if there's a lot of friction if there's a lot of friction you might roll down the hill here and just get stuck at the minimum um the minimum really are places the minima really are places where the field would just be constant if you started the field over here it really wouldn't be constant it would it might roll down if there was friction and there is friction in cosmology if there was friction then it might just come to rest at the bottom over here if it comes to rest at the bottom if the field comes to rest then it's constant that's the situation in which you can pretend that the field is very constant and doesn't change with time if it's sitting at the minimum of the potential it could come to rest in any of these all right so here is what it is thought that the potential energy of some field which we have never discovered we've never measured it it is a conjectural speculative construction with a field energy with a v that looks something like this now perhaps it starts with a shape of some unknown kind but then it gets very flat not completely flat question so the field energy doesn't vary for very much over some range of phi and then all of a sudden it comes to the end of a cliff comes to a cliff and falls down it doesn't quite go to zero and then turns back up now this is so ridiculous that um so contrived let's put it this way it is so contrived that it almost seems quite ridiculous nevertheless this is what observational cosmology seems to demand so here's the picture the universe started in some unknown way in a way that we don't know with a field energy vfi that was located on a plateau like this because this was almost a flat plateau phi didn't change very much with time it changed very slowly like being on a very very shallow like this eraser on the table top here uh there's enough friction and in fact in cosmology there was a lot of friction that the eraser doesn't move very much you could tilt the you could tilt the uh the table quite a bit before you would start to move off um the kind of friction is not quite the same as the kind of friction on this table here yeah more like a viscosity yeah more like a fluid viscosity this is called slip stick friction which means it sticks until it slips all right motion of an object through a liquid or gas uh is a better analog for what happens uh for cosmology so but there is a kind of viscosity viscosity is the right picture there is a kind of viscosity that's particularly associated with with an expanding universe and the faster the expansion the bigger the viscosity and so if this were a particle moving on a potential energy surface like this in other words just a potential like this it would slowly slowly slowly move down here under the combined effect of the slope of the potential that means a little bit of a push in this direction and at the same time the viscosity would keep it moving slowly it would stay at this level for a long period of time during that time v didn't change much so v was almost constant during that time and if v were constant then it would just be a constant vacuum energy so to the extent that the universe slid down this hill very slowly and the vacuum energy didn't change much then during that period the universe inflated during that period the universe exponentially grew and it exponentially grew with a time constant that looks like this where v of phi was just the value of v along here a very big value right what's that a very big value well it depends on what units you're measuring it of course so if you're measuring it in ordinary everyday units it's enormous even if you're measuring it in elementary particle units it's very very large but if you're measuring it in plank units it must have been it was very small so it depends on what unit you're talking about but in units anything like the density of energy in this room it's it's humongously big right so very very large energy here what's causing phi to move what's causing phi to move it's changing the slope of the potential the slope of the potential is causing it to slowly drift down that hill roughly as if roughly as if you had a weak gravitational field forget the talking about ordinary gravity imagine this room were filled with liquid filled with honey and you put a rock in it the gravitational field would correspond to a tilt in the potential energy potential energy higher at one end than at the other end higher up there than it is here the viscosity of the honey would lead to the rock falling and it would fall slowly with a terminal velocity all right so this slowly slides down here assuming the slope is small enough until it gets to the edge and at the edge here it suddenly goes over the edge and winds up eventually down here okay what does eventually mean eventually means today isn't that more like slipstick no no no it doesn't it never sticks well i mean it looks like it's slipping he's slipping no stick though right it's not just at the station right i always thought a slip stick was a thing but a slip stick wasn't the thing the slip was slip or stick slider with a slider do they call it that yeah so they do okay okay yeah i guess from my engineering background i thought a slip stick was a thing but no this it's a it's an adjective slip stick friction all right it's not slip stick it's just slip or viscosity and then when it gets to the end here all of a sudden the potential energy changes rapidly that means effectively that there's a large force on the universe pushing it over the hill here and what happens when it gets down here when it gets down here at the minimum it comes to rest comes the rest the combination of friction and minimum potential energy it comes to rest where are we today we're down at the bottom how do i know what the height of this potential energy is because i know today what the uh what the hubble constant is so the hubble constant is 8 pi 3 over g v of phi that's the exponential growth of the universe today and that appears to be down here the coefficient down here is very very small much much smaller than it was up here why this is true we don't know we really don't know but we do know what the potential energy is at the bottom here because we know today what the hubble constant is today right and it's very small we also suspect and there's some evidence that the potential energy up here was very much larger and that the universe that the hubble constant was very much larger in other words that the doubling time of the universe was many orders of magnitude larger than this one doubling every 10 to the 10th years in fact with standard cosmology cosmological numbers uh this inflation took place with a time constant of 10 to the minus 32 seconds or something like that so it's kind of crazy i mean this is a crazy picture this is a crazy picture the amazing thing is that it that it seems to have some validity we gradually drifted down here and came to the edge and went down to here the expansion that took place up in here is called inflation it's called inflation where did the big bang happen incidentally the thing that we normally call the big bang the big bang happened after we got pretty much down to here after we slid over this edge the big bang meaning to say what i mean by the big bang now is the surface of last scattering the surface of last scattering was very late in this picture it happened well after the universe settled down here so the big bang and everything we actually can observe about cosmology was down in here but before the big bang happened this period of exponential inflation took place according to theory and during that period the universe stretched itself out so much that all of the wrinkles disappeared if you like so that means that the universe at the time of the big bang or the time of the surface of last scatting was already stretched out by many many powers of e how many powers of e that we don't know for sure you can ask a question here uh the wrinkles are mainly wrinkles in the in this primordial scale then or and also the gravitational field also the gravitational field yeah in other words the shape of space and its curvature might have been fluctuating but also fine yeah what is the x-axis is that t or a problem why here in this phi the field phi this is the potential energy as a function of the field phi the field phi can depend on time as the universe rolls down this hill well it's sort of what acts like a time parameter like a what it's acting like a time parameter here because you've got a monotonic function it is in fact acting like a time parameter uh this is true time parameter meaning to say that it's monotonic function of time yeah what is the part after that all we know is that we're living at some place where the potential energy is not quite zero yeah nothing in our experience tells us very much about here looking back in the past we discover something that looks like a motion like this we're going to come to what the to what the observational evidence for this is but uh this may be a bad analogy but when you're looking at gravitationally derived potential energy it's a function of position but holding potential energy in the presence of a gravitational fielder weightlessness there is no a gravitational field simply in this context means a gradient of the potential energy well where what is the analog of a gravitational field in this picture where is there one okay let's not get ourselves confused between gravity as the real thing in this universe and the model that i was describing of a rock falling through uh through honey right right some force on a system uh which pushes it from one place to another basically that's the gradient of the potential energy here the fact that it's not actually exactly flat just in case it was not clear this was not intended to be exactly flat it was intended to have a small slope it's analogous to the table having a small slope if the table has a small slope then the potential energy differs from point to point and if something is on this table if there's no friction what happens if there's no friction it starts accelerating okay what happens if there's some viscosity it reaches a terminal velocity it starts to accelerate but then reaches a terminal velocity and just moves slowly across the table if the table has a small tilt it will move slowly okay it'll move slowly until it gets to the edge of the table okay and then it falls off so it doesn't oscillate well it may oscillate down at the bottom here that's dark that dark energy dark matter today all right the big bang and everything we historically know about the universal all took place after this got down to very close to the bottom here also down at the bottom it fell down this and just stuck there not stuck because of stick slip but stuck because it's the minimum of the energy and what is the period of inflation this balloon is expanding is that just the clip or the whole thing no no the whole thing here and that's about t to the minus by a minus two six that right minus thirty two seconds doubling every 10 to the minus 32 seconds now that may seem very fast but on the scale on the plunk scale and units over plunk time it's very slow in fact the plunk time is 10 to the minus 42 seconds this is yeah right we don't know how long this was and so we don't know how long this inflation took place so we don't know in that sense whether it expanded by a factor of 10 to the 10 to the 10 10 to the 10 to the 10 10 to the 10 to the 10 to the 10 to the 10 we don't know all that information got wiped out by this expansion now what happened what did this expansion do it did exactly the same thing that it would do to a balloon it flattens it and it leads to a situation where by the time you get to here incidentally falling off the edge here is called reheating there's nothing really about it it should just be called heating but it's called reheating why is it called reheating this happened rather suddenly when a thing like this happens rather suddenly the energy that was stored in the field is rather quickly converted to some other form of energy when you fell off the cliff here just like that eraser when it hit the floor there its energy its potential energy was converted to heat then as you roll over the edge here and by the time you get down to the bottom the universe is hot it wasn't hot up here in fact any heat that might have been there to begin with was diluted by this enormous exponential exponential exponential factor so if there was some thermal energy to begin with the universe simply expanded so much that it got diluted to the point of uh so that's why it's reheating that first curve up there represents an injection of heat well or something right right but we all we also know we know nothing about that right it's a hist you're perfectly right that perhaps in the very early prehistory something happened over here that was heating and then reheating but we know nothing about this really we can't observe this directly all right we can't or it's hard to observe we don't know if we can observe it but we don't think it's lower right right so how we go how the universe got up here why it started up there we don't know but we know that if it did start up here and it stayed up there long enough that the initial conditions are sort of wiped out or that diluted so much that we have no fossil memory of them everything started very very stretched out which means the universe was extremely homogeneous now this is going to be qualified we're going to qualify the statement i'm oversimplifying a little bit sort of on purpose if the universe expanded by a factor of 10 to the 10 to the 10th then it would look extremely flat by the time you got to here that's the reason we believe that the right solution of the cosmological equations today involves flat space remember i told you earlier on that observationally the curvature term this factor k which can be plus or minus one or zero is observationally zero meaning to say that the universe looks spatially flat to about one percent or beta better than one percent but it seems to be spatially very very flat geometry of space seems to be euclidean geometry why is this so well to the best of our knowledge there was a period of expansion which flattened everything out so that we are today looking at the universe on a scale which is very much smaller than its curvature we might as well use flat space because the universe radius of curvature is so much bigger than the region we can see all right now good question yeah when you say 10 to the 10th century or is that just an arbitrary number or do you mean it at least that big i i we don't know we don't know anything about how long have we remained up here we don't we don't know how wide this plateau is and we don't know how shallow it is the shallower it is in the higher we don't we actually don't know how high it is we don't know how broad it is and we don't know how all right we have some bounds we have some bounds we know something about the combination of these parameters and basically what we know is that the universe doubled or got multiplied by a factor of e at least about 50 times do we know e to the 50th do we have any idea how much energy got put in to the system uh we have some bounds on it we have some bounds on it that's another way of asking what the height of this is yeah yeah we have some bounds on it um i would say the best bet would be something like about 10 to the minus 14 in planck units but that's a huge amount of energy in ordinary units so you want me to give it to you in joules well i can't give it to you in joules without sitting down doing a calculation but it's 10 to a large number 10 to the 90th or something why did the universe reheat after the expansion slowed down well it reheated because it came to the edge of this cliff and that potential energy was converted at first into kinetic energy of the motion of the field just as this eraser that's potential energy got converted to kinetic energy and then when it hit the floor where that energy go to well it went into thermal energy it went into thermal energy uh and that thermal energy is the energy that uh that the universe had at the big bang yeah you made some sort of comment about dark matter uh some connection with dark matter you could ask might this feel of oscillated here that oscillation energy conceivably could be the energy of dark matter it would get diluted the energy of let's not get into that that the i did say that but the this is not the important lesson here can you say anything about the actual value of fee at the present which is to say at the at that v minute phi you mean this distance v or phi these vertical fee is horizontal what is the value of v relative to row zero no no no no no v has the same units as row zero that's v all right exactly that's row zero very small could you plot phi as a function of time yeah i could plot it but let me just draw it instead i mean let me just put my finger on here to follow it maybe it came we don't know very much about this but it slipped down here and then very very very slowly inched along here while it was inching along here things were exponentially growing and eventually it got to here and perhaps it oscillated a few times at the bottom but there was a good deal of friction at the bottom due to the expansion of the universe and so eventually it just came to rest at the bottom and then t goes on the tree stays still right okay right in other words as when you get down to the bottom here you've gotten on to this branch of things which is today's current deciduous base uh behavior now do we know for sure that that it comes to rest here no but but we know that it's moving slowly so this is this is a model of what we we know we know fragments of this we don't know the whole picture with any great certainty but we know some fragments we know for example that this is not zero so the universe is exponentially inflating today but with this very long time constant we know that it was rather high over here many orders of magnitude larger than it is today and so the universe did apparently i have not talked about the observational evidence yet but the observational evidence and indicates that along here the universe grew by at least a factor of e i said e to the 50 usually it's quoted as e to the 60 and but you can you can play with the numbers a little bit so the universe is e to the 60 times bigger than it was over here at least at minimum now how many times incidentally the number of times that it got multiplied by e is called the number of e-foldings e foldings and e fold simply means multiplication by e each of which took uh 10 to the minus 32 seconds but that also that number is dependent on the height here and the height is not well known the height is not well known what's known is that there was at least about e to the 50 or more e-foldings sorry 50 or more e-foldings is it possible that the uh that that it was absolute that was flat on the top and that there was just sort of the perturbations of the field which flipped it off the edge if it's too flat on the top yeah it's not it's not consistent that it was completely flat it had to have some tilt but uh but it could be pretty close to flat no possibility for some kind of quantum effect to flip it off to the well flip it off the cliff yeah yeah yeah yeah no no no definitely definitely so that you would just have uni sort of in this vast matrix of nothing you'd have a universe here if it were too flat at the top if it was the two flat at the top it would have created two in homogeneous universe which was what i was about to explain right okay so we know that it could have been too flat on the top so let me explain how we know that first of all i said this is an interesting story with many parts and i i will not try to get to them all now but uh what i said was the universe inflates and the process of inflating becomes homogeneous homogeneous on any ordinary scale on a scale let's say as big as the horizon size that's not terribly big it may have had many more e-foldings than that it may have been stretched out by many many times bigger than that in the same sense that the earth is much bigger than the horizon that we can see from six feet above the earth incidentally what is the horizon from six feet above the earth a couple of miles i think yeah the earth is much bigger than that in the same sense our horizon not in the same sense but in an analogous sense our horizon is rather small on the scale of the radius of curvature of the universe which means it expanded and inflated many times larger than the uh than the region that we can see okay so it got to be by by this process of stretching it got to be very very homogeneous except for one thing one thing prevented it from becoming completely homogeneous and that was quantum fluctuations quantum fluctuations now we i we could we can delve into this a little more deeply but not tonight quantum fluctuations created just quantum mechanical fluctuations take what would have become an infinitely stretched out completely homogeneous universe and leave over quantum fluctuations of various wavelengths in here which are the remnants of the quantum mechanical processes which took place i will not try to explain them tonight but let me just say that after this inflation took place no matter how long it takes place it never really gets completely settled down to complete uniformity why quantum mechanics quantum mechanics and quantum field theory ensure that there is always fluctuations it's kind of an uncertainty principle thing again but the the the fluctuations were there even after it may have expanded by 10 to the 10 to the 10 to the 10 to the 10 factor there were fluctuations in other words the field was not completely homogeneous it varied from place to place by an amount which was controlled by quantum mechanics if there was no quantum mechanics it would be completely flat with quantum mechanics it varies from place to place okay now let's come to the central picture which is really what has gotten the whole subject very exciting over the last 10 years let me draw well okay here's the edge of the cliff let's draw that edge of the cliff over here here's the edge of the cliff what i'm plotting here vertically is ordinary space ordinary space x when i'm plotting horizontally what am i what am i plotting horizontally um i guess what am i plotting horizontally uh a field phi what i want to draw is the contours the contours of the field the contours mean the surfaces of constant feel like a contour map it's not a contour map of elevation it's a contour map of the field phi now if i was completely homogeneous it does vary with time here's what you would see at one time you would see a completely homogeneous field that would mean that phi is the same at every point of space here's space vertically here's the field phi is horizontal phi is the same over here as it is over here as it is over here as it is over here that means that phi has gotten very homogeneous what would happen with time as time transpired as time went on let's transpire you would roll down the hill which would mean that the field would gradually move moving to the right until it got to the edge over here when it got to the edge that's the value of phi where reheating occurs it would suddenly fall down and the sudden change in phi would fall down to here so with time if you plotted phi as a function of position it would be constant constant a little later constant a little bit later slowly drifting to the right and then if it were all that homogeneous in other words all that smooth every place in space would go over the edge at the same time if it were completely homogeneous but now let's put quantum mechanics in what does quantum mechanics do it puts some fluctuation into the field and so we could expect that the that the contours will show some fluctuation they will not be exactly homogeneous and as we roll down the hill some points reach the edge before the other before other points all right here's the way i like to think about it a bunch of imagine a bunch of uh soldiers walking in lock step arm and arm and they're walking towards the edge of the cliff all together if they are really very well lined up with no fluctuation in the rank in the in their location then they all fall over simultaneously but what happens if some soldiers are slightly behind other soldiers some of them are a little bit in front some of them are a little bit slow and they're moving really really slowly then there can be a long time delay between the time one fellow falls over and the time another fella falls over so there can be large gaps in the time between the time that the different pieces fall over the edge now when you fall over the edge when a piece of space falls over the edge let's just take a very simple situation imagine the field is homogeneous except for a little bump so the contour looks like that it gradually drifts to the right and this point over here falls off the edge before this point so a region of space is is created which has been reheated it's down at the bottom here whereas the rest of space is still up at the top of the cliff all the soldiers except for one uh four are up on the top one guy has fallen over now that one guy has fallen over that one region of space here is inflating less rapidly than the region up here the vacuum energy down here is small so it's inflating slowly down here and rapidly up here what happens what happens is the energy that's in here the new energy that's in there the new energy that's in there the kinetic energy the energy of falling off the cliff here is expanding less rapidly in space than the rest of this region out here so a little lump of energy forms a little lump of energy forms a little bit later let's say a little bit later another bump goes over the edge by the time this bump has gone over the edge this one has been over for a while and it has expanded somewhat it has expanded somewhat then the next one falls over the edge what does this lead to this leads to inhomogeneities in the energy density over here it leads to inhomogeneities and the energy density because different regions went over the edge at different times and their kinetic energies were expanded and diluted differently there's a particular pattern to the kind of fluctuations in energy that take place but what do these fluctuations of energy become eventually these are the seeds of galaxies the energy density is not uniform after you fall off the cliff and in fact the slower that you're moving the bigger will be the inhomogeneities if you're moving very very slowly then the time between this fellow falling over the edge and this fellow falling over the edge can be very large during that time this region may have grown and then when the next one goes over this one will have already spread out so the energy density will be most the energy density will be most variable in space if the field is moving very slowly would be the other way because the expansion slows down so we you go over you'd expand less oh it has kinetic energy yeah it expands less yeah and so that the first yeah yeah yeah i don't know that's right that's right that's right so yeah but right but the point is that it will create it will create variations in the energy density that will first of all come from the original variations in the field but then magnified by this effect that that one guy goes over before the next guy and therefore the effect is different rates of expansion in the two regions and that has the effect of making a variable energy density that variable energy density is necessary it's necessary because without it there would be no galaxies so it's a funny combination of inflation inflating the universe and making it very smooth but leaving over these little fluctuations which eventually became the seeds of galaxies now this is a highly quantitative story i'm describing it descriptively but it's something that can be quantitatively computed from the quantum fluctuations in a field and in expanding space and you can compare it with the properties of of the fluctuations which you can trace back from known galaxies from known properties of the distribution of galaxies you can trace it back to the earliest times right after this reheating took place and it fits it fits well yeah could you say that it was cooling and that after it falls it cool it doesn't cool as fast um no not that's not really quite right it's a question of expansion that that by the time this guy falls over this guy is already spread out and done some expansion no it's not expanding as fast that's right so it's a combination there's a competition of things going on expansion in the in this piece that fell over the edge and the inflation of this other fluctuation here and it gives rise to a pattern of fluctuations of energy density that was for all practical points of all practical purposes the observational start of the universe very homogeneous the later fluctuations are hotter or well they're cooler they're cooler because they've been stretched somewhat when this one the earlier ones are hotter than the leaders no the earlier ones have cooled some the next one that goes over you see when you go over the edge if a little piece of space goes over the edge it gets this much energy all right that much then that energy is diluted by expansion afterwards so if a little piece of space let's say that much space goes over the edge it picks up yeah it's always hotter right all right so then this one cools a bit and then the next one falls over it's somewhat harder so the heat so the the hottest places are the last places to go over the edge yeah so but that's right but the main point is that it leads to inhomogeneities in the energy density and those in homogeneities they're small in fact they were i mean observationally the variations in the energy density are one part and a hundred thousand variations right no this is this is primordial density fluctuations this is neither dark dark energy is this that's the energy today the feet you're saying includes matter and radiation yeah that's right it turns into all kinds of very hot stuff right matter radiation and that kind of stuff and it varies from place to place observationally about one part and ten to the five now that one part and ten to the five is not a number that we can derive from this picture that one part and ten to the five tells us some constraints on the shallowness of this how flat it is the flatness of it the height of it it puts some constraints on the parameters once those constraints are imposed then it creates a spectrum of fluctuations at different wavelengths different size scales these guys get spread out this guy comes next he's smaller in space and so forth so the effect is that that you have a fluctuation density spectrum fluctuations on different scales what happens to a variation in energy density that you start out with well if you have a bit of over density over here let's say over density and a bit of under density over here the over density gravitationally attracts material from the under dense region and so the over dense region gets more over dense the under dense region gets more under dense and the effect is to magnify the the spectrum of fluctuations so just a very very small little fluctuation to begin with will gradually build up depleting the under dense regions and increasing the overdense regions and that's the origin of galaxies so from the spectrum of galaxies from the spectrum of the spectrum from the distribution of galaxies in space one can try to reconstruct the density fluctuations that were there at the very beginning now the very beginning means after reheating and compare them with the theory that this picture leads to which is namely quantum fluctuations in the field being magnified by falling off the edge and then being processed by gravity the answer is it fits very well if it's very well uh with this picture and it's the only thing that fits very well with this picture so you have to assume that it's a fairly small volume at that point where that the observable universe is a small volume at which point galaxy formation for the time of galaxy formation the observable universe was some pretty good fraction of what it is today i'm not sure what you're asking me well i'm just wondering how fast this movement from under-densed over-deaths takes place oh well once it starts it happens fast is that during reheating no that's after reheating no that's after at the end of reh at the time of reheating that's when these fluctuations were first established in other words after going over this edge here there were some density fluctuations which were bigger than they were in here but whatever they were but still one part and ten to the five roughly one part and a hundred thousand yeah it magnifies by going over the edge you magnify the quantum fluctuations but then gravity still hasn't done its work gravity doing its work magnifies them more and eventually magnifies them a great deal and turns them into galaxies and stars and planets and so forth does that violate the second law it sounds like it sounds like entropy is going the wrong way it's not um gravity sometimes does things like that has that effect it tends to concentrate things yeah but it's not no it's not violating the second law nothing can violate the second law but it does it looks somewhat counterintuitive and that gravity is rather peculiar from the point of statistical mechanics most things tend to make things flat and evenly distributed gravity tends to make things clump all right and the clumping actually increases the entropy the ultimate is to clump them into black holes and black holes really have a huge amount of entropy yeah so uh yeah how is the microwave background reflected in all of this the lumps of the microwave background uh the lumps in the mic these yeah these are the lumps in the microwave background so mostly the mask doesn't really count that much it's the microwave background that predominates here well no it's it's that this stuff gets imprinted on the microwave background so um all of this structure all of the structure evolved for a period of time gravity did not become important until after the surface of last scattering gravity only became important after uh the universe cooled down to below the temperature of the surface of the sun so until that time the fluctuations were pretty much primordial right just these primordial fluctuations and they imprinted themselves on the surface of less scattering so that what we see in the sky in the surface of less scattering is pretty much these primordial densities those regions have to be far enough apart that the thermal doesn't wash them out before the surface of last gallery yes that's right uh you said that fee was a scalar field so that wouldn't be an electromagnetic field no it's not it's not an electromagnetic field so how did all this so the photons just went no what happened is all of this energy look what happens to that energy when that thing hits the floor there some of it gets converted into electromagnetic energy not very much incidentally most of it just gets converted into heat but the question is what happened when this field fell down here okay it got what could it get turned into what can that energy get turned into by the time you settle down at the bottom what could that energy be the only thing it could be is particles of different type that's the only other thing that we know that can carry energy is particles of different type so in falling off the edge here this field energy here presumably got converted into various kinds of particles those particles may have been unstable particles they may have decayed what did they decay into they decayed into electrons and positrons protons and antiprotons or quarks and antiquarks some photons and when a large amount of energy is deposited like that what does it do it heats turns into heat after a while it just turns into heat that heat eventually became the photons electrons positrons protons antiprotons that uh so the uh the reheating is actually where you get the manifestation of the uh is where you get watch you're getting inflation of the universe yeah and but it's at that reheating point where it manifests as a inflation in the mass and the part well it's where it becomes particles it's where that energy gets converted into radiation particles uh electrons protons the the details of this are not known the details of how you got from here to electrons positrons and so forth is are not detailed known the only thing you know is that when you have energy contained and are slowly expanding and incidentally once you got down here the universe was much more slowly expanding on the scale of the rapid particle reactions that take place the universe was very slowly expanding when you got down to here all right so what happens if you take a bunch of energy and put it into a pot which is very very slowly expanding well it comes to thermal equilibrium it somehow eventually equilibrates and turns into a thermal equilibrium whatever whatever the temperature happens to be so the details of what go on as you go across here don't really matter much all you know is a lot of energy was dumped into a pot which very very slowly expanded and that's enough to tell you that some percentage of it is going to be electron some of it's going to be positrons some of it's going to be whatever it is let me ask this how much of physical theory survives going back behind the medium pretty much gravitation and quantum field theory but none of the other physical ingredients exist mean up on the top here yeah right that's pretty much right no photons no particles of mass and no particles at all right because the fee has well the only thing that was there were these fluctuations these quantum fluctuations in the fields in particular the quantum fluctuation in this field phi and uh it's not worth calling them particles so the actual act of the reheating is that the the cause of the big bang or yeah that's you um yeah you may if you like think of the reheating as the big bang but it's still it still expanded many times over before it became the visible big bang remember it was so hot when it went over the edge here energies here much much higher than electron positron energies and so forth much much hotter than the surface of the sun when it went over here so the universe was still very opaque it had to cool down before it became transparent so when we look out and see the surface of last scattering that's very late on this scale it's down at the bottom yeah down to the bottom everything in everything that we can measure see observe happens at the bottom so by that stretch then when you have the quantum fluctuations then there are really multiple big big bangs right each one as it falls off is causing well yeah yeah yeah but well if you like but on the other hand these fluctuations are on scales anywheres from very very much bigger than the horizon to anywhere is much much smaller so some of these fluctuations were small enough in size that we see them manifested as galaxies and stars even planets that's probably a stretch galaxies galaxies and stars yeah when there's some discussion of acoustic waves and all this process doing some kind of stuff itself yeah um right i guess it has to do with the under density over density well this happened the the acoustic waves are a phenomena that preceded the uh the gravitational uh things yeah we should we're going to talk about acoustic i don't know i'll just we have one more class i don't know all right the acoustic waves are particularly interesting because they give us a measuring rod on the sky all right they give us the measuring rod which when we look out to the surface of last scattering i will tell you about the acoustic waves the next time uh you see lumps of stuff which were associated with acoustic waves whose size you know where do you know them from that i'll tell you next time but because you know their size and because you know their distance you can start looking at triangles as those acoustic waves which are manifestations of uh of the processing of these fluctuations they started to slosh they basically started to slosh and they created lumps and the lumps are of known size because the laws of uh the acoustics and so forth are known we know the size of them we know the distance and we can measure this angle that's enough to use some geometry to tell us that space was either flat positively curved or negatively curved and uh so those acoustic waves are important and i just it's too late for them now okay all right do we do we have another class i've lost track we have one more two more two more two more okay good good good good all right so the next time i will tell you a little bit about how the geometry of space got measured from all of this

Channel: Stanford

Views: 88,215

Keywords: Science, physics, Albert, Einstein, matter-dominated, universe, expansion, vacuum, energy, Hubble, constant, scale, factor, horizon, surface, of, last, scattering, Heisenberg, uncertainty, principle, harmonic, oscillator, kinetic, ground, state, zero-po

Id: KATSfJjZGVQ

Length: 109min 38sec (6578 seconds)

Published: Sat Jun 13 2009