Cosmology | Lecture 8

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Cosmology | Lecture 8
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(March 4, 2013) Leonard Susskind examines one of the fundamental questions in cosmology: why are there more protons than anti-protons in the universe today? The answer lies in theory of baryogenesis in the very early universe.
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begin inflation tonight hopefully will get through barrier Genesis we will get to it because so little is known not is the basic theoretical framework modern physics from Barry barrio Genesis means the creation of an I'll explain the words of a moment but it does mean the excess of matter that modern theory about I will tell you what I know about the history of it was engaged in the history of it the 19 80 Sybase Demopolis and I were asked by Bob Wagner why is there so much entropy in the world by Wagner's a cosmologist at Stanford White is the number of photons which is counting the entropy in the world was somewhat larger than the number of protons and electrons in Member Tibet entity 80th times larger not to the 10th time sorta tend to 8 times larger than to be 8 times larger approximately 20 8th and 9th something like that what is that with clearly released broke we thought about a little bit and then realized that the question was upside down the question was not why there are so many folk dance why there are so few were there are so few protons and electrons that we basically work out with the modern theory is going to play with tonight and for a brief period of time these conditions for explained the imbalance of particles and that particles recall the euro Demopolis Suskind conditions somewhere during that time but later tool young Russian mathematician came to me and they said they are writing a book about 1 writing a book gather where they will not only writing a book they were looking for contributions to a book after celebrating Andre suffer roars career and they brought me a list of papers about this thick when I look through them and see what was interesting and write about it so I started look through and sure enough I discovered exactly the same paper it was meanwhile the believe saying as worked suffer some I have done with the exception there was better 1967 13 years earlier they lost completely 2 armed the Western world the Russians know about it but to you that was not a communication between the Russians and so all I did indeed right a little historical paper about sufferers contribution and made the mistake of calling him the Sakharov conditions there now known as the sufferer could jut justly so of course that the article was a sufferer of conditions and they're basically 3 conditions and go through explained to you that if they are satisfied and they are satisfied our then there will be in balance Our matter only entire matter be real question is magnitude it this is only this is discussed encounter questions become operator is that they were asking really AT a legitimate question OK maybe the world just started with more particles in nearby articles and the story but it focuses your attention all lot when you have the numbers when you have a number of specific number in this case it was it can be a photons for proton numbers you focus your attention this numbers needs an explanation so our excess and itself was as a factor Dakota said well maybe just that way but wants as a number of particularly the numbers some oddball number like tend to the minors you start to think maybe this thing needs an explanation sold half the explanation of the young that and or roughly speaking for a black body our thermal spectrum the entropy is simply the number of photons it's just a the number of and black body about black body radiation carries entropy thermal and the within those some factor of water 1 fields some pie a simple factors entropy black body radiation it is just a part of it is just the average number of folk Thomson when people speak about beat entropy of the universe will and many contacts with the often talking about is just the number Of the cosmic microwave background photons that's a bit me so when I say when when 1 Bob Wagner came to me and said Why is the entry b of view world so large he was asking me why the number of photons for Proton it's a launch you you might ask how that had that small number protons make such a large number of photons but that it's not the right way to think about as pointed out to last time or 24 in the very early universe that with huge numbers of protons and huge numbers event that brokers and they were basically equal to each other and with a number of protons and number that protons being approximately the same of quarks and by quirks sink drew for electrons and positrons being approximately the same as the number 4 times thermal equilibrium of some very high temperature and that a cold when cold the font times with leftover they will leftover because they couples the universe became transparent than the 4 times just hung around and we see them today the protons and hint that protons annihilated each other the universe expanded primly slowly and that was plenty of time for them find each other by and large and annihilate each other and all that was left over 1 of these slight excess so the question became not why there are so many photons but why was kind excellence of Pinto the minus a another words the number of protons minus the number of can't by protons where number of India divided by the number of photons but the number of photons and early history of the history of the universe was approximately the same as the number of protons passing by protons number of protons plus and P and that's a number which is about 10 I think the summer and say OK so there's a number to compute White is a small number of peer now we don't know what the number war the reason for the number that because we don't have a complete theory but almost any theory that we write them which explains it always gives a small number so we'll talk about that what kinds of conditions are necessary for necessary and turns up sufficient To make an imbalance matter over now is a matter of a hint that matter how comet Pinkham our matter over matter what's largely a definition that's largely a definition which 1 would the thing we call matters a thing there were made out of bonds sold that's the by let's begin with a hypothesis which is really believed to be wrong but will come through it namely that Barry on number was barely remember means if there are only Proton bounty on number of and be interpreted in terms of quarks and basically the number of quarks minus the number of and by quirks in the world I think it's 3 times that the exact reasons 3 kinds that is because it was originally defined in terms of protons and neutrons being barrier islands and the proton and neutron has 3 quarks in it so what's called beta Barry on number of world number minus the number of it but 4 times 3 if all the big the city and left where yes the vibrant by
3 thank you letter 3 but with off 3 times the barrier numbers yes you caught me divided by 3 barrier on number of protons is 1 has 3 quarts but OK so that's cold Barry on number ANW there are other kinds of objects that can be Barry on No. besides protons and neutrons but unstable the neutron was unstable unless there are other kinds of objects weaken mostly focused like thinking about quirks themselves if we like and the statement that there's a ban on excesses statement that they were worry in the early universe more quarks and intact quarks the number of quirks Symantec work separately were about the same as before bonds and so will the question is how it got that way OK let's the suppose for the moment the bounty on number is like electric charge 1 of the things about electric charge is considered it doesn't change with time now barely number is not like electric charge electric charge is the authority Of equal long forces longer-range electric fields which create long-range electrostatic forces barrio number itself is not a source of some kind of cool type force of course the protons are electrically charged therefore they make conventional probe of conventional Fulham forces between each other they make electric fields the neutrons are not electrically charged they don't make electric fields so what we would say he is it's a charge of the proton that the battery on a number of it which is creating any kind of long-range field and barrier number itself may be concerned that may truly be because but it is not exactly like electric charge it doesn't exhibit this tendency to make long-range forces by but I suppose it conserve deposit conserved then if there is ever and excess in the beginning of the universe whatever that means there will always be an excess and that excess will be of frozen even if you change the number of ports you must change the number of works by the same amount if barrier numbers conserved and what's more experimentally barrier number appears to be highly conserved nobody has ever seen a proton disappeared Our we can talk more about experiments which search for the decay of protons and but the 1st approximation our world protons are extremely stable what could they dictate to with this request what could be supposed that Proton was indicate what could be key to domesticate things which are lighter than itself Our must take something which has a positive electric charge of abrupt on what they think and must therefore if we want to assume however tool stable there's really only 1 thing that could decay to it could be Kate for positron and something electrically neutral print could decay a proton could disappear and become a positron that considers electric charge a dozen conserve energy a positron much much lighter a proton but it would compensate by giving more often neutral particle what kind of neutral particles around folk guns photons are a prime candidate so a 58 possibility for the proton would be proton draw a kind of fine and diagram proton moving along with full-time which will call gamma for times of typically called gamma and an electron and that particle plus that's a possible thing that could happen and we don't really know any deep fundamental reason why can't I and maybe that's how we talk about us have secretary get does happen but for whatever reason young no it kinda and meaning of positron neutrino nobody knows that OK on neutrino is a fairly on tool family owns maker bows on a proton is friend so whatever the proton decays too it must be Kato something with an odd number of firming up so it can't became into positron and NATO and neutrino right now very very yet it was there that you could always geek if given any conserved quantity you could always make up a cemetery that there but then you could say well alright is there is really a cemetery and way test it is always square the barrier numbers so it it's over it's a little bit circular but yes you're right there barrier number was conserved it would correspond to a cemetery and is not considered that that doesn't correspond to a cemetery OK now is there are being part of the matter in each other's by my head for time and that all asked the yeah so that Is that that gave no that's not became homeless advocate of the proton just called annihilation of a proton but important point here is that the barrier number doesn't change 3 quarks and 3 and back works came together over some talk of a two-year barrier numbers is 0 and a Woods is just a bunch of photons barrier number still 0 so right so that's a fair question but the but and you could you could call it a decay if you wanted to but wouldn't correspond to radio back OK so for whatever reason an elite we don't know the reason really Foley of the standard model does not permit this incident doesn't happen in the Standard Model for versions Our extensions of the standard model which a perfectly viable in which over this process could happen now 1 thing we know about it immediately the decay rate of the proton cannot be very large Howell a proton Sabine around 15 billion euros or reduced 13 . 7 billion years and they haven't disappeared on us so that Tecate time of the proton Warren microsecond or even faster over which particle physics might permit the just wouldn't be here anymore so that they did the lifetime of the proton police very very very long but in fact it's much much longer than is necessary for the protons to still be here be mean lifetime of a proton is more than 10th of the 32 years it's very long we don't completely understand why impact on y all but we take it as a fact a fact of at least a temporary fact let's assume it for the moment that would mean that the problem barrier on numbers in the universe but let's just say in a in a box a box doesn't change and so the only theory of this excess that we could have is it was built from the very beginning and still survives today that would be a consequence of Barry on conservation barrier number conservation enough saying the stroke I'm saying that consequence a barrier on conservation that this is the same today as it was at the very beginning now there was as another symmetry of nature which again is not really a cemetery of nature but you might have thought about it as a symmetry of nature at the time the staff were off put out his theory was only a couple of years after it was discovered that it wasn't the cemetery talk about it but it's particle impact particle reflection symmetry the statement that particles interchange with that particles that you can't tell the difference because you could tell the difference between a proton meant that broke because we made at a proton but if we she'd all of our proton stand that protons if you will for made out of and that protons and
I was made at a proton circuit to close and somebody showed me a proton I would say yes that's a proton somebody showed you that Proton you have exactly the same response there would be a new would see the same thing that I saw that's called particle and particle symmetry of reflection her charge reflection symmetry and for technical reasons fight that's that's a cemetery it's not symmetry but up until 1964 65 forget exactly when it was thought that charge conjugation symmetry see was charged conjugation sent saying those believed that it was a secretary particles go and that articles told other things which was thought to be symmetries of nature which went along with or called P which is P is for parity but has nothing to do with economics are for fairness it left right symmetry mirror reflection symmetry that if there's a kind of particle which exhibitor handedness for example it rotates right when it moves forward spins the right where most forward then it had been assumed that they would be they left spinning particle which also moves forward left right left-right symmetry and that was called parody and the final interesting symmetry for us tonight was called T and T is kind reversal what this means is that any process that can happen in nature Justin ordinary Labatt restrict ourselves the laboratory processes let's not worry about the whole universe a process that can happen in nature we could take a movie of it that we run it backwards is a part of it is still a possible our thing that can happen anything they can happen the opposite can have now it doesn't seem that way when you think about the real world of course the 2nd law of thermodynamics things as things get worse but the microscopic level worker truly microscopic level we don't average over things and we don't lose statistical averaging and so forth any process that happens in nature was thought that it's time reversal was another possible bomb thing we could happen that's called kind reversal symmetry now is actually not mathematically This is a mathematical statement about quantum field theory which I am not going approved tonight it's a horrid theorem but follows from the basic structure of quantum mechanics relativistic field theory it is not that charge symmetry is symmetry particle particle not that parity reflections Cemetery is a cemetery all or the time reversal is cemetery but the product of all 3 of them P fee of 20 what that means and CP team is a cemetery and this from mathematical reasons fundamental mathematical reasons Jewett you'll have to accept for now is not consistent to rulings and not have the symmetry was a symmetry mean immediately begin a process replaced every particle bites and particle reflected in a mirror and run it backward is still a possible process in nature and you have to do all 3 in order to be sure of observatory up until the sixties we are all set for later but she just said she not cover to say decided there's always a case that is those changes said you don't see that from assuring equation Sharia equation from I decided by detainee equals a these 2nd sigh of IDX Cuero something like that that's not quite right following it changes sign of that changes sign left-hand side but doesn't change assigned right-hand side so changing this kind of thing doesn't work but at the same time you complex conjugate a change which also requires you to change signed on for complex conjugation that does work but that that this this is something we only get into right now CPT user some drink but let's the polls from moment was go back suffer robbery before suffer before a big factor actually let's suppose that is the charge conjugation all are see kinds P which is the usual 1 the people focus on that that was of the cemetery seek times change every particle to that article and left him with a right here that was actually thought Toby a good symmetry of nature that would entail some kind of symmetry which allows you to change a sign of every particles particle article it also change laughter right of that goes along for the ride if you believe that when you might as well do it if there is a complete symmetry between particles but particles why shouldn't be at the very beginning was an imbalance of 1 vs. br that nobody can tell you there isn't an imbalance that just dates back at the very beginning but you might also wonder you know what's going on here the laws of physics seemed to be completely symmetric between the 2 kinds of things particles and particles and he for some reason it was this small imbalance of size tent of the might save it doesn't sound good but doesn't sound right to be modern theory of barrier Genesis begins with the idea that there was a balance of particle in that article were balanced again not for any good reasons are just for whatever see whether initial condition you started with the was no biased or particle and that subject they can be justified in some some frameworks but that's so that how is it possible that that it got balanced the only way that it's possible for it to get a balanced Farm Bill Elliott possible further getting balance is if the conservation of barrier numbers is not correct and other words if process Eastern happened and he is 1 the processes can happen in nature in which a proton becomes a positron that is a violation of barrier conservation which allows the barrier a number of the universe to change that would be the 1st requirement for a fury of Barrio Genesis that was based on the assumption that the initials of the starting point was balanced between the 2 of you go wind-up with an excess of quirks over and back for of barrier arms over and that barrier variant mean protons and neutrons you must have a mechanism which violates the conservation of Dallas sakharov 1st condition lesson number or Sotirov conditions suffer all conditions start number 1 diary on number of violation violation means violation conservation and as an example the process of a proton becoming a positron and a photon is an example if it happens in nature condition warned let's village just talk about that for on if barrier number 4 conservation is not a good conservation laws of physics
then it must be very very weakly weekly broken 1 as I said protons are very old they didn't disappear so it must be very all must be very or photons or old hands whatever mechanisms such as this kind of decay it must have a very very very small probability per unit time 1 can current series currently unified theories which do with some of which most of all affect everyone not I think that back every known unified any villain and that the fire the coupled to gravity every known fundamental theory violates Barry nonviolent about conservation like this you can ask is known theories why is the proconsul stable and a cancer cases to be something like that theory has fined diagrams has processed use it which the proton comes in from the left me from early How goes electron of photon but somewhere in the guts of this fine diagram all kinds of particles let's not specify exactly which ones are in the air but among them assume that there's at least 1 or more particles which are very very heavy and other words that requires a particle type which is very very heavy particles which had not been discovered yet no other reasons to believe this is the standard model by itself With its ordinary known particles does not permit this happened and so in order to make it happen you would have the have no additional particles that were not part of a standard model and that certainly means a their heavier because they have been discovered yet but imagine making them very heavy how heavy all 10 of the 16 GVU Kansas 16 times heavier Proton which is not natural number for heavy particles then what's true it is that this kind of process is extremely unlikely extremely unlikely means that the quantum mechanical amplitude Florida is suppressed by immersed powers of these of this heavy met typically for example it might be a scoreless standing remains in the final diagram will contain 81 over him square just because it's so hard to make a heavy particles just because someone likely that heavy particle doesn't last very long it has to pass through our melt into the rest of the finding diagrams but particles heavy enough in there then this will be a very very small probability process that's what dried that's what that's the kind of thing which keeps the proton stable In modern unified theories don't of right I'm not saying it's right but this is a mechanism that the extra particles that there are all heavy enough that they suppress enormously now novel say something else let this 1 over and square if for some reason proton is giving a lot of energy some of this is really well over and the square but it's really some energy and my some energy squared if proper has excess energy from some other place for this will be a much smaller suppression not tell you where that extra energy comes from the minute worth can come from but under a world of proton sitting around with nothing to give it at an enormously heavy kicked enormously high high kick it doesn't have a huge amount of energy protons Limicolae everything else don't have huge amounts of energy so this is where you begin and a series of this height can explain why the throat stable of course you could say no explain anything they just tell you have for some reason that deserve B particles which could cause promoter necessary for proton decay must be very heavy and extra house that so yet energy is not included in its rest mass squared nevertheless we going here are play with such energy could come from a moment but as I said all theories all theories and prevented the city and theory that ever will exist will have the price of the possibility of violation OK so let's agree tentatively barrier on violations is not Cabool that process such as this can happen not forbidden by any fundamental law of physics is just an accident of the particle spectrum of the proton stable as it think that that an assumption working assumption battery on violation by itself it is not sufficient to want to give at em average excess protons over and that protons why not because every In the end wears it every event like this which can happen which could cause you told Louis proton number as a source of decreasing Barry on number you started with when you live here you have no units of via the every process like this there is the charge conjugate process in which an aunt that Proton comes in 8 electronic Troy electron goes off and he and by particle the photons the photon that part of photons itself so if we believe and particle particle symmetry benefit process like this his apostles like that happens and on average on me an average there will be as many of these kinds of cases these kind of case we started out if we started out with equal population of quirks and that quarts of Marion's and barrier islands and we tried relying only on the violation of barrier number it would not be a very efficient way to create an excess water I mean by that I mean think about affirmative supposing that there was randomness that the notices or might did something else incidentally in the very early universe there were lots of electrons positrons and photons around perfectly possible for the opposite to go an electron positron of photon can come together and make a proton and electron NATO photons come together making it so there's a as a statistical balance of things going on it's only statistical that director would be as many protons and that disease processes a statistical process but on the imbalance Our protons and that is not a statistical effect yacht Laura died all that insiders that members of this here get negative 1 ghost 0 0 now right leg or most 0 0 here warned those 0 end and the reason that it can be a statistical effect is that it is quite true that a barrier on excesses a small number 10 of the miners but he asked how many armed hung linear protons are there in the entire universe known universe observable universe and the answers about the ATF how they would you expect the excess of protons over and that broke Beaver were simply a purist statistical effect square event you know that these statistical fluctuations in the variable just due to random statistics is of order the square root of the numbers you have a young if you have a random random heads tails flat and you collect the let's say a thousand of flips the number of heads will be 500 but that up 2 of the margin of error and what is the margin of error at the margin of error is the square root of the number of flips and so you expect that the number of flips the number of flips will be of the number of heads will
be 500 plus some ideas what's squared 525 by a margin of error be about 25 OK now let's come to the world which has hinted he 80th protons and what it is the margin of Aero audio statistical fluctuations average expected the testicles excess of protons will be square root which will be because the quality of right to the flooding had the 40th over the 80th is 10 to the minus 40 so if the excess was tantalum minus 40 years because could be statistical but not much much bigger than that young b because of the work that 1st yeah that in all of them but that if there 60 young but broke that is it is good because these other thing I would be very hard to justify extremely hard to justify his of was statistical fluctuations why it would be the same everywhere that would be very very hard right right you expect a patch over here with protons a patch over there with that protons and so you can ask what is the experimental evidence that the neighboring or be this very distant galaxies are not in a galaxy and as I understand that these movie was very good evidence the good evidences of the population of other galaxies was a symmetric between galaxies and that galaxies than you would expect cosmic rays of especially high energy cosmic rays which are thought to be cosmic an origin to have as many nuclei as an technically harassment Nucla and that nuclei as nuclei we do see for example of helium nuclei and cosmic rays of as I understand nobody has ever seen and dying nucleus because regret you do see that Proton but that's fairly easy to explain even if we just had even if we didn't have any cosmic rays but particles coming in when a high-energy particle who would be atmosphere would make him 4 times for it's extremely difficult to make an entire nucleus that would take an incredible piece of locker of a very high energy collusion with the atmosphere creating and nucleus not likely so the complete absence of nuclei strongly suggests that the universe is not equally populated with galaxies and galaxy so this something go explain that's not statistical and we need to to explain I have to I believe we said I believe that helium nuclei in cosmic rays directly from around you don't detailed statistics are but I don't know it's not my field of physics but firm but that's where the argument lies we 1 minute OK Our we also don't there's another if if if our galaxy for example was particles and the Andromeda and that particles in the in the region in between you would expect there to be bold particles have and plenty of electrons around for example circulating around the region between galaxies you expect it to also be plenty of positrons and then you would expect it to be a lot of positron electron annihilation and positron annihilation positron electron violations are very easy to detect they produced pairs of photons are very definite energy and those pairs of photons there could be observed and where it's not that we don't see electron-positron annihilation but we don't see nearly enough of it to account for the possibility that neighboring galaxies will be by galaxies solved that almost certainly ruled out that there I and I galaxies out there and certainly ruled out as an equal population of them OK so particle in that particles symmetry kid suggests rather strongly that the universe was created symmetrically although it doesn't prove it the the next element of the argument is that in order to account for the fact that more protons and think that this charge conjugation symmetry must fail the idea that the other particles in intact particles are symmetric and the laws of physics and that the charge conjugation times parity enough that it would be bad enough charge conjugation or charge conjugation together with anything else any symmetry involved into changing particles and particles if you have that you would have a very hard time explaining another way to say it is if we allow young we allow bearing violation that's not enough that would just give you the statistical effect you need something the push it in 1 direction you need something the bias Of course particles rather than articles you need something in the laws of physics that will cause this barrier on violations of bias so that 1 kind of thing happens more than the other implications of that art that you need violations of particles and by particles symmetry and particularly the so-called CP symmetry but basically just particle and particle symmetry again is their particle and that particle asymmetry in the world yes theories we know with absolute certainty experimentally that particles and particles don't behave the same way after that particular example that surround these examples are hard to come by but want to have 1 or 203 you know that the laws of physics math symmetric between particles particles these simplest example to explain is the so-called being as on a big mess on is a particular kind of particle made of a pork and meant that Quark it's made of love it's made of AT and the above violent Quark end a and in a downpour bottom quark and nearby down of course I'm talking about form honors on reform measures on the bound it's called be particle now has it that article you just interchange be bottom quark fully and die bottom court and the down and die down quark for downpour and you get the me in mayors on both the Beavers and the impact it has on electrically neutral but they are not alone in that particles this 1 is made up of b Cork and end by down quark this was made of in quirk and bound for Robey sir what's right these particles and they decay until pioneers has arms but status for her received yet fixes father's right out to strike down 1 possibility arm From what I forgot what was on the case and big Kayenta lots of things but bomb charge all I know they decay into it came as on an apartment on and I think the Mazzotta becomes and think it's a cape lost Hi my guess is not for the factors that is a very definite decay into a came as on partners aren't being as electrically neutral so decay products are electrically neutral that it follows that the entire and decay into the entire particles which is and negatively charged came as on and positively charged ions no important thing is that's a process in which a particle indicate the other particles versus a process in which the in that article also became whatever that particles that these are the rates for these things happened unmeasurable they are
measured and different there are different while the user can remember which 1 is about there were 2 thirds of more
important than the other so it's it's in this case it's a fairly gross violations of particle impact particle interchange definitely real effect there lots of indirect above measurements has been known for a long time the particle in that particles symmetry is not a good symmetry is not symmetry but 1 said that wants this can happen once this can happen we case I need to say that there are fundamental processes in nature buried deep inside Fineman diagrams somewhere that are in balance between particles and particles that's no longer the case that Mr. decay and that became a half to have equal probability theory is a rule is a rule that the help will decay rates that Cobol half-life of proton and the and that Papa and have to be exactly the same that's a that's euro from relativistic field theory but the way that these token be different from each other is is more than 1 way that a proton indicated proton can also decay for example into a new class of photon Anthony and that from time indicate into mule minus a photon want says that if you calculate although possible ways of the proton decay indicating when you consider the half-life or the total rate the total rate of decay of the proton it must be exactly the same as the total rate of decay of the entire broke but does not say is that the decay rate of the proton to electrons auto positrons of photons must be the same as you know what I mean it doesn't say that any particular decayed pasta have a symmetry in particular that some fundamental level the this charge conjugation symmetry is violated by something in the theory that it will allow this and not equal what here not people who special similar Justin and did not equal to allow that and Ali allows it basically insist that they used to be once that's true it says is a biased somewhere in the laws of physics there is a bias toward either protons oriented probe 1 matter versus some kind of bias and that's something which is absolutely necessary that a the barrier the violation could give it directionality together need a push in 1 direction the other so sign for us 2nd condition incident thinks Succos papal was forgotten when CP violation was 1st discovered but sufferers papal was very quickly after that when the CP violation of particle in that article symmetry was discovered and not be correct within a year or so I remember exactly Sotirov wrote down his basic condition of X number 2 see CP your article and by particle asymmetry to laws of physics but this is expected in any theory that we know a theory that we studied a particle physics always has and indeed including Justice standard model in fact I said something wrong the standard model does allow barrier violation economic allows it insists on hog at some level so it every theory that we know about that as theoretical statement insists that barrier number violation have experimentally we now CPU violated a particles partial and by particles symmetry now 1 remaining gaps still if if the the favorites said In light they of the because the because the new particles heavier than the electron so we could be in a situation where Armed with Kabila situation for example were Todd enough however after court or by would need to explain to his 1st wife this happened rapidly even North said that the Proton was very stable has to do with the environment Monica Monica back To be questioned right on How we all had only overcome the fact that the proton so incredibly stable remember what I said the protons life time is something like about 10 to the 33 and 34 years or longer the universe has only been around for 10 10 he was sold on that scale the Proton is very stable and why don't we get to ignore this kind of thing and the reason has to do with the fact that the universe it's very early stages was very very high because it was very hot the protons of quarks and particularly substitute quarks here it doesn't matter because it was very hot they were constantly engaged in very very high energy collisions a high energy collisions meant that the photons moving in this plasma is very hot gas had lots of energy how much energy it depends on the temperature probes some temperature you get for high enough points where the average kinetic energy the average extra expectation on the of a proton is high enough so that even these heavy particles here do not suppressed the proton decay or the barrier violation will force deployed short of a proton at rest crew to get arrested it is clearly a proton in environment where is constantly being knocked around and having a enormously large excess energy of some kind or another is very stable bullets heated up the high-temperature a high enough temperature this excess Matthew it is not an important factor in the proton decay would happen quickly so if we go back the very early universe when the temperature was very hot then known Linda then these kind of Prosser sees command now this statement that the pope will decay rate is same for protons and protons is a statement of 0 temperature statement about a proton arrest in an environment where has no excess energy is being kept on In a when it has extra energy then that is not necessarily the case that generally not the case in an environment which has some energy around which is kicking the proconsul around decay rates don't have to be the same song aid wrath that is not part of the problem
has to do with CPT symmetry is I said that there was no particle particle inversion symmetry but there it asymmetry different at least of all known quantum field theories and all alone quantum field theory string theories and not right down which is as relativity and quantum mechanics bill charge conjugation of reflection Williams time reversal again what that means is you exchange every particle for pretend that you reflect a member of a new run the film backward that it is a asymmetries of all theories show what is mean that means are among other things that In thermal equilibrium of the universe was just static if it wasn't changing but was hot and thermal equilibrium in thermal equilibrium what time is the same as backward time and thermal equilibrium backward and forward in time of the same the same thing as no asymmetry of time reversal so In thermal equilibrium with the universe is not changing imaginary universe which is a stop part which
is there hot a hot pot it would have time reversal symmetry and it has time reversal symmetry and that has seen times he times he made it must have seemed tree CPE just means particles change article for our purposes of particle and that article and time go state was a saint by time and time goes Mike this time that's a good symmetry but the world has no bias toward 1 time or another they just stuck again you'll back the having a particle particle symmetry and you cannot have a proton and that Proton excess in thermal equilibrium that's a theorem that's a fear known for long time that in thermal equilibrium that thermal equilibrium will come to a configuration with equal numbers of Procomm dealers was not the thermal equilibrium at early times it was expanding was expanding fast literary time was expanding fast enough that it could not be considered in equilibrium and it's not an equilibrium that means that for a time backward time a different stance theories of the universe is expanding forward and backward time where are not the same so In a rapidly expanding phase of the universe we don't have to worry about time symmetry it is definitely not a matter of time symmetry is broken just by the expansion of the universe and we're in business and we have enough asymmetry of all possible kinds that the barrier on violation allows a change in the barrier the CP violation allows directionality for it and we approved what I elderly equilibrium out of equilibrium yup it just means things are changing rapidly in a particular direction of time may be universe is expanding fast enough that's all it means so that run the thing backwards does not look like the original thing in a world where the uterus is running in 1 way namely expanding loss is out of equilibrium they have equal and that has to be enough out of equilibrium it's not enough for it to be very very slowly expanding it has to be expanding rapidly enough that these microscopic processes don't have time to adjust themselves to work the equilibrium configuration but whatever whatever that means it means that backward and forward prime on a different picture of the universe exhibit at a movie of the universe allows you to tell which way forward and which weighs backward in time just by they felt by the expansion and the fact that cooling effect at early times it suddenly cooled suddenly cold rather rapidly beginning that's enough to completely ruined that reversal symmetry and at the time reversal symmetry is ruined the CP symmetries also relatively solved those are the 3 conditions of suffer on all 3 are believed to be really satisfied in the real world also believe that they are enough that of all 3 of these are true that is really just no way it would be a complete accident with no rationale if there wasn't some some excess created the problem is that nobody knows enough about the physics of the early universe the physics of very high energy collisions the physics of very very hot temperatures the nature of the particles in here are the details of what drives the CP violation and so forth nobody knows enough about it to be able to make calculation of what the imbalances can't stadium that simply we don't know enough so we know it is all 3 ingredients that a bomb Prague necessary probably sufficient to explain in balanced growth of their but the ingredients needed to make a computation show that this number is head minus 8 times in Q plaster and bar that's out of range we don't do that that's a status of the servers particular problem a surgical barrio Genesis and it will be a wait a year a much more detailed theory of both early cosmology and particle physics of very high energy any questions about that we're not finished with a barrier the fact that we know that you may say as much puts constraints on adapt to deduct adducts Omri it does but not to use you're right but that the noble and my knowledge of his used in a really effective way constrained things if too many variables some things young right of hundreds of parameters of reduced Omar about now that these like that that is a severe blow that I don't see it man for man is elect me every time a proton disappears above positron appears president them out father most of the loss of barrier number must be made up for by an increase In turn right or the increase anything that increases pain will decrease was 1 all the process to use that thinking about conservative the army electric charm there's no alternative to the statement that the barium number shifts 1 way the Alec charm excess must shift the other way right now bird flames that is not big enough I was like No way I do believe there are no reasonable remember form Our I just them a little bit skeptical that anybody really knows how to do the calculations our that says that I am a little bit skeptical you know my involvement in this indeed with stating these 3 conditions and that thousands of people not about maybe tens of people started to try and make computations based on a standard models of Stephen Wolfram was 1 of them and he invented Mathematica I think the calculations well enough I look at what is no way that they're going to be would do this because there are just too many unknowns about universes for solo it it may be correct that I don't know or have followed this the story for a long time and it may
be that that we know the CP violation in the Standard Model is too weak for a drive for wants to admit CP violation into the physics altogether is no reason do expect that high energy it might not be tens and hundreds of times larger once you open the door to it so that it's no longer principal then you don't have really much much control if we had some of the show only after we see today 1st that well I'm right I'm sure that's right could have been a population in in the very beginning which was balanced between OIC witty saying well and they ended and that sense yes and that shows that you could not hold analysis in the opposite way by thinking about electrons instead of the protons and there is no doubt exactly it how about the word the lingo barrier Genesis is sort of historical relic Her are so we did is that he's failure at literary was Lula were can very that while it has moved back from neutrinos arrived people focused on the barrier on the North of our we had was that unless they say number as solid because of where they can cities number for the ratio of barrier a number of protons 2 photons but that end but has a a lot of violations that there was a lot of annihilation between protons and have 4 times that basically removed almost all the protons and in that time but that was the point at which the temperature fell long enough power that process that would create protons an impact farmers a very high temperatures is very high energy photons photons come together and they create warmly remembered a proton and the nearby those photons have have enough energy to to create a pair protons and means they have to be at least 2 GTV worth of energy as long as it temperatures high enough these things are going on backward and forward in equilibrium along as long as there are enough high energy photons around To be able to cause a proton and that time who appear and because of the way but then when the temperature falls below a certain threshold there simply aren't enough high energy photons around to create protons and that protons protons and that protons could create photons of massless protons event that protons have lots of energy can go this way but it has a hard time going this way so once temperature falls below that threshold the protons start annihilating each other but was not enough energy to of course were talked on Monday and that Proton collide and make photo on those photons have a lot of energy but then they just go out into the open their energy gets lowered by coming equilibrium with the lower temperature background stuff sold as the temperature goes down the number of available high energy photons decreases and you can make the proton at that time but you can go the other way so that point that's when the annihilation starts and eventually All-Pro time that protons forget the giddy now if it and when Noah went nowhere arms it that it's all about clearly yet I was that was quite early hours before nucleosynthesis Our temperatures in the DGV range I'm not sure exactly what spot here is on death row in the 2nd match at work can be afforded by the time of the manner and beat contribution will revert to a yes now prayer said after all this violation on this aid to those articles they go back to level with my role in 80 of them for a report on work because remember that radiation energy density decreases like over the scale factor of 4th power and matter energy density decreases like 1 or a few right Silver is years veracity article workers models can visit does now but yes there were 2 fish then civilian areas there start initial offer Shin board How you war effort may lose a what is now a matter of hours outside G tho I see what you mean about yeah yeah it's so yes yes drug maker figured the quickly flounder on the fact that at some point the universe was very hot and at that point there were these loads and loads of peas and be bars at least if you want to follow standard thinking about the bar Germans are dead what's and very very hard to explain why would be that people particularly since CP violation is as a small export from Bavaria ones they be grossly unequal and given mind these decay rates very small but OK I will move on and that's what's known about matter and entire matter imbalance the universe has said no think it's be too soon that we know are more right now next that we want to move on is inflation inflationary universe the inflationary universe the idea was put forward to explain another 1 of these things which it's not entirely clear needs to be explained for wasn't entirely clear that needed to be explained at the time and leak question was
why is the universe so terribly homogeneous and isotropic this became erratic critical issue when the cosmic microwave background was discovered and the cosmic microwave background quickly became a rabbi high-precision saying the high-precision thing being in short order the EU read black body Carruth had been measured the temperature of a cosmic background have been measured carefully was known to be 2 . 7 degrees and with some precision with some of the error bars fairly small microscopic Calabar Riviera borrows just they can be seen OK so the temperature was very well-defined looked like a plant distribution like a black body distribution almost exactly exactly Roger Patel but moreover it was a scene in every direction so suddenly this rough idea that the universe is isotropic became a high-precision idea this took years I'm convincing history and told some smaller but at least by today in any case on the idea that the universe is isotropic very very hard precision thing so you could ask why is the universe so isotropic on maybe it's isotropic must have been isotropic very early for no particular reason why wiII and isotropy alarmed penis the distribution would be would decrease with time in fact quite the opposite lumping this tends the increase with time because of gravity gravity patents tends to take along and magnify the size of the magnitude of the lumps so our missile means the universe must have started very early being extremely homogeneous and isotropic when savory earlier I needed before they would galaxies before they were on planets at a time that the black body photons times originated with coupling time numerous was extremely I that it was of course not that it could be completely isotropic or homogeneous if it was exactly homogeneous it would stay homogeneous anything which is exactly uniform allowed to revolve our state uniform you this is not uniform with for galaxies and clusters of galaxies that has long been that there will be there clearly was much smaller to begin with smaller in magnitude for the simple reason that long this tends to increase with time we just explain what I mean by that you start with a world which is completely uniform was it stays that way but let's suppose it was a little bit of over density here a little bit of all the density that's that's a little real a big region of barely big region where the density is all little bigger and neighboring region what happened what happened in grad and gravitational theory is the opposite of what happened in other kinds of theories another has a series with tens the happened is as if also a density here it will diffuse out and be eliminated for example you have density of each dropped in the water divorced what happens over time it refuses then there are an and disappears becomes homogeneous In the gravity of the opposite happens in the argument is very simple if you have an although density here because gravity is attractive universally attractive who attend to attract the stuff around it pole in decreasing need beyond the density outside an increasing it inside another with a scanner run runaway situations around situation where a little bit of inhomogeneous will tend to reinforce itself so if you have over densities under density of advanced under density and so forth some however the tendency of gravity will be because stocks stuff out of the under dense regions and put into the all advanced regions and thereby magnifying the greedy Our in-home originated so the fact that we see in the language of today does not mean that the uterus very early wars as inhomogeneous geniuses of history we must be much less inhomogeneous just by running short backward in fact cars modest early were able the estimated by running the theory backward they were able to estimated at that time of deep coupling just how much inhomogeneous you was there in order that the galaxies could nucleate out of that inhomogeneous erodes the picture is the universe was very homogeneous but little bit civilian homered in a little bit too ripples little bits of excess depletion access depletion of some kind and those of advanced regions eventually collapsed by this mechanism form galaxies and clusters of galaxies and be on the band's regions form voids and that's what we see today saw you can estimated that was estimated by people Jim Peebles and other people early cosmologist sixties and matter-of-factly when how much In a moment maybe was necessary at the time of the coupling and the instilled wives his away you quantify if you look at the lumping there's and you characterized by a Delta role away Del Toro is roughly the needy excess stands an alarm relative to the background and he you divided by the density itself as a fractional over density in a typical advanced region the 5 compared with density itself that's the dimensionless the measure of how much How much shown in home virginity there was then was pretty early recognize that this was a number had to be about 10 to the minus 5 somewhere between 10 miners for America's flies so we were again with the same kind of situation a question why is the universe homogeneous workers at really require a mail to started that way but now with the number was a number in addition to just saying the universe was homogeneous is also clear that it wasn't homogeneous it wasn't homogeneous with a specific numerical magnitude forward I want to others to specific numerical magnitude you want to know why that now it's not that we learned why this is a matter that we did not we do not really understand why this is the right number of Harlem but the existence of this number focused attention on the question and the 1st question was why is the universal homogeneous later worry about why it's inhomogeneous the 1st order of fact was that was very very homogeneous these explanation of that today he was lower chair seemed rather far-fetched was put forward by Alan booth in 1980
was the universe simply X ended by many orders of magnitude and of course when something expanded stretches and if you stretch out if you have an inhomogeneous universe with lumping and you stretch out enough you'll make it homogeneous at least on the scales Berger relevant so the idea was the universe inflated which means expanded and in particular exponentially expanded for some period of time and stretched itself out so much bad Is there a flattened itself to to the outside blond literary like blowing up of loans the loser crinkled rougher a shake thing collapsed to blow up and bearers stretches out and flattens out that's a that's an analogy which you shouldn't take too far down a sysop bear more will be missed greater Texas in different directions yeah it's not exist we look at some of Iran's role in the book isotropic to me I look out on an average over it was like the surface of the year it's full of hills and mountains valleys so 40 rather explained to them by geological phenomena and so forth but on the whole Europe was very smooth and the uterus a there is homogeneous there were 4 of homogeneous I was saved homogeneous that it's going to be isotropic they said a rash headed to a massive while as set out of but it's a random process but expect some action it the city although no it's not a random it's not random it's not random I see what you're getting at you saying If Hillary and you might expect that someone was out there would be large over advances it's all random was some statistical probability you might find a large lump because it's not random the don't talk about pattern of it basically it's a narrow imports are from How could not squeeze is down to its size and the minus 5 relative the background on the whole it's very small but nevertheless there are with in the size of the wheels are very small what the implication is and there are uniformly distributed through space there are a homogeneous isotropically distributed there no large tremendously large lumps out there all very small small magnitude of small size but smaller magnitude and so were more or less like a very very smooth earth were thoroughly reports on the way it is In a related both he and those gave of up that each trashy pulled from during inflationary period temperature was not important aspect of things during the inflationary period temperature was not terribly relevant factors the lawyers exponential expansion which was the single most important thing and her to begin with where are we still have a few Aruba time to talk about some preliminary use it looks like next week will be our real week for inflation the equations and rent ticket through the basic equations of inflation sure works detail but I think what I want to for the rest of the evening only Estella section but section have village anything from has everything to do with everything but tonight and his current of friction the equations of friction Red Baron because I will use it as very simple what I speak of friction speaking of discussed to be thinking about something go like stones falling through a viscous fluid Why am I doing that there's going rat because it will come stone following the water off honey Fernandez reminding you of the equation is for its following it tool 80 force which is a gradient of potential energy let's call what's called a height here which I caught under qualified which is a stupid name from a height but it's not a stupid name for a field and as you might expect him felt about the fields but nevertheless the analogy is why is the height of the storm and a force on the stone those for some the start which is related to its potential energy in this case it could just be the potential energy of gravitation in but let's just call it a potential energy of 5 that's a forces downward which means via fight increases the upward direction and what is the Forest Forest is the derivative Of the potential energy of minus it minors the derivative RVU with respect and just a derivative ordinary derivatives DVD 5 progress writers equations now known as equations for the Ferrer rougher simplicity let's just take the stone family unit what's the equation emotion ethical said May the force on the right-hand side is miners DVD fire and that's equal the message of setting a global 1 finds acceleration which is fine double got a 2nd time the river of 5 OK this is pickles MAC and is nothing special left by in uniform and a uniformly force field which we just mean DVD fires I can't stand the start a formal for the uniform acceleration that just very quickly pick up all our speed and continue accelerate me that has ignored the viscosity of the fluid that's moving in which I say something I can't find Abby that means that there's another force right inside ya that other forest is 0 if the
object is arrest the viscosity has exerted no force object at rest moving through the fluid which creates the forest and sold before us on the right hand side is depend on the velocity the larger the velocity the more the viscosity and a simple fluid viscosity is actually proportional velocity itself so as a force on the right-hand side which is proportional to the velocity which direction it's obviously opposing the velocity so it's got a minus sign in front of the media a fearsome coefficient in front of it that's called the coefficient the isospin number I forget what's called but thank right for whatsoever for home delivery Remele beat beat gamma reverence get said of yet why not use of force as it slowed down those who really 5 pushes Barry right there is moving with the downward vertical velocity right there is moving with the downward vertical larceny them means fight negative right minus fiber was positive this forces out as long mowing down as always OK for set to With naked that that's what he did find that is negative DVD finds there was negative but this 1 was positive positive because 5 negative for now so in the beginning when the storm starts to fall 5 . 0 and basically it starts out accelerating exactly as it would without but very quickly fight that will increase and less as you moved down the forests get bigger and bigger rapidly this is going to increase because 5 increasing until imbalances DVD at that point the forces canceled and that's called the Terminal velocity in particular if these if the forces uniform of the downward force for example force of gravity is uniform near the surface of the earth the visitors scored F minus F minus 5 . Hammer that's a total and at some point it stops accelerating because these 2 balance each other and of course that happens when No. 1 and 5 . reaches the terminal velocity and the Terminal velocity 5 . is equal but now I'm getting my confused the forces that is negative right the forces negative causes down but the Terminal velocity happens when F 5 that as a former Gamma number signs are confused the of a problem here your arm pulp mill which Ortega f is negative so Terminal velocity is negative thermal losses negative causes for an armed that's the basic theory of friction and what does it do it slows things down in particular their via 580 has a shallow slow via file plus 3 of 5 plot try this way supplies far-right follow horizontally even notifies vertical direction but plant horizontally and I suppose via Pfizer rather shallow Hill it a rather shallow healed and the viscosity coefficient here is large be stoned falling who along with potential energy he will simply take a long long current rolled Hill that's the situation we will want to be here and fire will not be a stone that not be be the position of the stones it will be the value of a field ah we will want to be in a situation where an field evolves very slowly be costs a lot of friction and that will drive inflation and will come to it I think what sure to go 1 better and I'm a little afraid to Earth over do it tonight OK with that so what's gone for a little bit gone through a bit but let's go on from there now organ a considered the classical field theory numerous is filled with some field this field is going to be a scalar field now with Aziz come from what scalar field it was may not was simply made up in order to be able to explain the isotropy and homered in unity of the universe at the time this was created it was a long shot forever crazy idea but it seems to be right so it is the idea the world contains addition to the electromagnetic field the gravitational field and all the usual fields 1 more field it's a scalar field and it's called me in for hours 5 white because it has to do with inflation now aren't willing to assume that is pretty much uniformed space weaker summits not uniform in space but as a space expands it will tend so what to stretch out the variations and Pricilla just assumed for simplicity fine is uniform in space and she think about energy stored in a field and a scalar field of this type love everybody remember what we energy of me the energy density of 80 of a scalar field is contains a kinetic firm was kind derivatives is the energy density containers his energy density of to score to score the energy of a scalar field contains 1 term which is fight that squared this is just a Connecticut energy of the field not the Connecticut the sense of movement in space but the ever since Due to prime the parents they typically there is another term which it has to do with gradients in space partial is right before I square is also turned and the which have to do with gradients despite gradients space also store energy but since we've assumed that the field is homogeneous and is not varying space which we could justify later our there are no gradients space and so this is the only terminal energy density has derivatives and other things that can be there is a potential energy a potential energy which is plus V of fire it's just the thing that made up that different values of the field
have different energy doesn't have to do with derivatives just in having a field of a given magnitude is an energy density associated with a car that's called the field potential energy it's not by accident that I'm giving me is the same location for ideas field appeared was quarter stuff but now this let's follow the field and must follow it in a box in expanding box there's always the box that we focus on is expanding with the universe and how big is it in any given time how big is that that box is a of size Q the scale factor killed the city unit boxing coordinates space the size of the boxer's a Q this is energy density This is the energy density to get the energy every railroad energy here but this is really energy per unit volume if I want to write energy of a few Member box are after multiplier but AD is time-dependent depends on time so we have a time-dependent energy expression in a cube of tea Connecticut plus potential energy you could think of this if you like as will formally mathematically being seen as the most as as energy of a particle kinetic energy pose potential energy except where the coefficient our view which depends on time something you wouldn't ordinarily right down you might have a mad asks for a situation where they will be armed with a massive a particle might depend on time and then this might but ordinarily would write that down nevertheless that's all we have women energy Connecticut plus potential let's assume 180 nor is just back if it was OK if there was a spatial dependence we will have he returned for spatial Grady let's assume for the moment that the field is uniform space it it's not eventually it will be because the expansion will stretch about and get rid of the gradient structure a stretcher out solo that's reasonable to assume that after a period of time there of Aron O'Grady O'Grady of the field space the set we're thinking associated with that yes yes yes yes but if we assume that uniform then we all we need to do to find the total energies to multiply by the volume of a box which is time dependent on they for that had set up at the time now solve if a brawl losers I'm so used to it that they think of it as so obvious we have to solve the equations of motion while that's like asking about like asking what happened but was a roving up moving down that will depend on initial conditions it will depend on how long we wait in the especially depend on the sign of DVD 580 namely the size of the force delay a where simultaneously but now we can we can back off that study what happened but this is the easy problems the study OK now how we find the equation of motion when we know the kinetic energy and we know the potential energy the various ways we could do it but there are the most efficient way is through a branches equation grungy strike the Lagrangian our program and is the difference of kinetic energy and potential energy solid you pick up your copy of the theoretical minimum annual look up little references equations for this 5 like the coordinate fighters like the and here is the Lagrangian only new thing that wouldn't be there for ordinary particle is this 80th prior rats were Gabbard branches equation the 1st turn is deemed by IDT I suppose we can make it IDT off sure els with respect to fight got theory but remember that what some right-hand side right as 4 branches equation was sold Pasha Lovell with respect 5 . versus the equation we get a partial those fight that just justified . kind 8 cubic feet this is partial of echo with respect to fight back this isn't here yell buddy 5 . is 5 . 4 terms in a tube of tea is obvious now but now we have to take its time derivative IDT and that we have to set equal to 80 cube times Q. trends DVD Friday what just ordinary derivative DVD 5 we could call fiery called for Simitis DVD fire we could call the forest but notice that Is Exs extra explicit time-dependent thing as isn't quite look like Newton's equation was there would be no equations of a was constant players not transparent so it's work it out and see what it is 1st of all the Debye IDT there at 0 Tier 1 comes from hitting 5 . pl comes from hitting a Q so let's 1st the first one the first one is a few times fiber robot and that's Debye IDT of 5 . 4 times a Q What's a 2nd but if I die find the time derivative ridiculed the time derivative of a Q is Ferrari ace glared at times a dog where right yacht at an parentheses over here and that's equal let's just call it a day ADQ who'd times the force the forest on fire retreat very tempting and I will do it to divide helping a since it appears both here and here west survive out killed but never divide over here also Kerry so rats a clean up its fight double . plots for got over it maybe a square divided by a Cuba's well over a year so it's a doubt over 80 times a fight . physical death it was a bout of a called in cosmology the Hubble
constant which is not generally a constant it's H but of course I everywhere is space but not necessarily inclined may be the same in time but it may not be possible comeback Jordan his family given might could be time-dependent 8 double sorry with a double about fiber double but from here plus 3 8 times 5 . equals f strike us witness way plus heat calls this is exactly the same equation as the falling stone With viscosity coefficient 3 H & R force which is just a the gradient of Salam model for the way this field evolves can be envisioned just supposing that find was the position of particle on a halal where the height of the hill was vie for the gradient of the of the altitude of the hill was force DVD fiery ball rolling down a hill except that it is a viscous drank force proportional to the Hubble expansion rate so the Hubble expansion rate behaves as a kind of friction and that is why we went through this exercise over here if the homily at the Hubble friction it is strong each is believed and the force here and the feel is reasonably flat not terribly flat but some are flat and this could be like a ball moving through them Our motor Arroyo and in Wisconsin on a cold day take it just left to its own devices without the friction termed it might roll down the hill and a few sect With the large friction that could take years to roll down the hill depending on the magnitude of the friction so this is called the cosmic friction terms
and the equation of motion of a of a scalar field has the effect that is simple effective slowly down the evolution of the system in keeping were there From rolling down the hill the next time we're going to use this to study orgy a universe which contains a field like some auto remote look at me FRW sorry Friedman equation are within energy density which is given by the of the study a study how the universe expands and evolved under the influence the energy density which is slowly slowly slowly rolling down the hill here as the phenomenon of inflation at the radio 1st responses very small slowly moving field OK next time for more please
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