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Cosmology  Lecture 9
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a deeper and more profound questions I'm sorry I sports OK they yes we would get a review a little bit required world was in place in the finals I get BAT file down the ladder plans young to be defined so what's what is back and so forth forces we think you down bike To put it you however fielders a few like electric field magnetic field in this case a hypothetical fund discovered field which is a scalar field scalar field exists in space a off yes a scalar field in space and that feels that energy electric fields of energy magnetic fields of energy scalar fields of energy the energy depends on the value of the field of research this is an undiscovered field we don't know how the energy depends on the field Zuppa let's was hypothesized vertically but plot energy in the field of accord these fans the potential energy for reasons I'll describe a moment but just think about it as energy that would be stored in space prelude of or you'll be energy density that would be stored in space just by virtue of the fact that the field which I'm flying horizontally here as a certain value if the value of the field 1 value than energy is 1 thing of the energy of the field has a different value the energy is a different thing and so forth and it's very much like we me electric energy magnetic energy stored them electromagnetic field but different different it's a scalar field makes big difference for something I thought plot as well nobody's ever experimentally detected its on discover make after graft just to make up if it now you might think well this is funny if the field 0 shouldn't be energy B 0 but the value of the field which is 0 is somewhat arbitrary power the field has not been discovered I don't know where 0 is aware have 0 energy Celesta's plot and make it any of them and we don't know what this is really a fight and arm it represents a source said the energy chemical potential energy and the reason I call a potential energy now is because its energy that is not associated with time dependents the field it's not Connecticut Energy that's not energy that's associated with kind derivatives the field defines a certain kind of velocity that's not velocity of something space it's the velocity of the field itself another words kind derivative of the field the field has a certain value at a later time it has a slightly different value than has any a 5 . that's a little warm Of the derivative of the position of something think of the value of the field as a quarter it's not coordinator particle which of its value of a field changing with time away from the OK and it's changing with time there is view of energy an example an example a why not just as elastic strain the elastic strain is a kind of field in a onedimensional world the elastic strain left elastic stringers vibrating then by virtue of the fact that each little piece of the stringers moving this kinetic energy recalled the height of the string position of the string of recalled a fight that would be a fight that EDIFACT here would be Connecticut energy of strain which would be proportional fight that squares just like fact we usually define to England dominated this would be the kinetic energy of analog of the kinetic energy of the field now if this were a particle who would say I recognize this is like 1 half in these squared where M. Williams is even a Fight Club a it's not a gin your message just call parameter R number number or level for a number aid size about better yet In squared trade why is it that it yet because I 1 of the picket square root that's why but but growth that 1 half and these squared with the role of the mass of the none of the massive particles being replaced by and squared well at 5 then the field of IT the name of the field and instead of calling it 5 I redefined and new things were talk all kind of like experts exits Kite Greek symbol caII and I said equal to end times 5 this subject over here just becomes kind so I can call at that time the square of the time derivative of some field having been illustrated that doesn't matter would you call coefficient you could always eliminated by a change of our definition of the field let's not father was just put a 1 here that's the kinetic energy of the field we said is also a potential energy source the couple field energy time this fine and now field energy means the energy contained within a small unit boxer Littlewoods energy density really but let's follow a small box in which the field energy is given by threats from mathematics Arif is isomorphic isomorphic is the same Abbas the mathematics of a particle with kinetic energy potential energy or are very close to it as will say and if this were a particle if this were accord minimal particle would not want equation right down the throats of the stepped off the steps artist say this is the energy Carlos Connecticut pose potential corresponding to it there is a grungy and energy corresponding to it there is a grungy and storm grungy and His kinetic minus potential energy 5 . squared over to minors via 5 and then this will grant his equations just remind you of Lagrange equations look like they were bright IDT a derivative grand jury with respect to a velocity in this case the velocities fight got is equal to the derivative of a Lagrangian alarm record script our word from propelled works continue recalled the fell over here over here as minus will grant him with respect for the quarter slow granted his equations he is Lagrangian we can work it out of the river that will grant him with respect of fight not batches by . differentiating Square just
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give you something and Togo's away so the alibi if I got fired back and differentiated twice friendship begins with respect time is becomes vise doubled 2nd time derivative by another with the kind of acceleration the acceleration of the field itself simply defined to be the 2nd time derivative and that people To be held by farright because the Lagrange Ian contains might the potential energy instead of plaster potential energy kissed becomes equal minus the derivative of me With respect the flight crew that with this world particle and fire was the position of the particle then DVD by defining it would be a derivative of the potential energy with the position and that's the thing we would call for a 5th of function of fight just as in general before some object depends on its position it might be constant various subject falling in a gravitational field near the surface of Europe forces pretty much constant but that doesn't have to become bribes or this is basically the equation of motion for a field box and I was still in the field is not very much space the reason we can get away with that cosmology is bigger spaces expand locked or assuming spaces expand the lot the variations of the field of gotten stretched out and eventually they get so stretched out that over small regions of space over box field is very very smooth flat assumption about this it is the field equation for a scalar field with a field potential energy fire at said equations now this is I was answering a question but in the process of entering the question start the lecture the threat of it OK so let's let's go back now this object on here is energy density this or here if we actually want energy in the box we have the multiplied by the volume of the box so let's keep them trying and multiply by the volume of the box and the volume of the the expanding cosmological box the proportional ADQ right the scale factor killed it was a matter if the scale factor didn't depend on time scale factor didn't dependent time would just be a numerical constant and numerical constant in the Lagrangian just cancels out of both sides no matter what it is time dependent so the kinetic energy and potential energy both have In front of them 8 fueled of time same will grungy when you go from a energy to Lagrange Ian kinetic energy minus potential energy you have to include that factor of a few volume better way to say it is that this was the Lagrangeville Vince city the density of the grungy in which you have multiplied by the volume of formula branches now let's go back and redo the Runge equation of stood no correctly including me a few 1st of all there is again just for comparison or the over here on the blackboard PLO by . is not find that anymore but 8 Q and 4 . 0 we sought a few of 3 times fog that's deal by defied got and then we have to differentiate that With respect prime just differentiated Debye Duty that's the lefthand side of the equation variety in side of the equation is Q times will minus sign DVD 5 SARS here except as an 8 killed in front of a line so they could see immediately if AT were constant we could call outside derivative here and just factor at our throwaway cancel out from both sides of the equation but because it's not constant we have story about it and in particular when taking derivative with respect to time is going to be a contribution coming from the timedependent Cibecue that the new thing that's what the expansion of the universe does the equation of motion for a scalar field expansion but the mood Sharon works calculate that promotes calculable voters by IDT on this subject here has warned turned which is just a cube of tee times fight double that's all that were again we would cancel it from both sides of the equation and we beat just dealing with
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ordinary particles the 2nd turned his time derivative of a Q all times fight back so it will fight back outside over here and multiply it by the time derivative make you so time derivative but a cure arraigned a square a box create a square got ponderous 3rd your you get that that's equal killed minus DVD fight now we can divide by a for derived by 8 resource goes away with security but we have to divide hereby ATQ Commack Carramar minute this rules or archaic cell a square of a few that's called warmer an . already is what the hobbled thing he sparked constant her right to us the bubble thing I on so when we get we get the equation if I double . plus 3 8 mind in general it's time dependent 3 h times God equals mind this DVD fire which I called previously are earlier I called it efforts Corvette became minorities and the derivative of the the potential with respect to
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field itself so all the hair would be as if they were off Wash pushing the yield down the hill and so forth so is always pushes down a hill but would be pushing forward over here backward over here so OK that's the basic equations that U.S. newfound now you of continue question bad we can figure out a physical interpretation is ready with 55 visualized path is a force derivative the potential if we don't think of it as a force of what they get the plays the role of forest in the equation of motion and since we're doing as a general form from mechanics mechanics field now mathematically all of these properties of a force but what's not in space pushing some object of forests pushing the field toward lower potential energy the tendency for the field to world who moved toward to accelerate toward law potential energy OK this is our equation emotions and the interesting thing is interesting thing of course is no Tournier in exactly the properties of a viscosity this equation now becomes the equation of 8 of the the field but think of the field that was the position of a rock just for as an analogy a position of a rock position rock which is falling there's as a rock is height will call you fight I'd above the surface of the earth lower ever and it's falling if falling what they are under the influence of of forest f which in this case but taking pushing downward exactly like we Our forced to gravity that means the potential energy use increasing upward and therefore the forces downward it but behind that's all that was we would expect the equation to be acceleration is equal before the mass widow that away we got rid of by review armored redefinition so the subject would accelerate and dinners show shot a couple of seconds a sold removing hundreds of over 100 meters a 2nd faster I out fix plan to get behind leaders 2nd but not much time there which is always a way of it is following the water or even better let's say something even more viscous than water Honey with I think it will gradually sink but it won't continue to accelerate I'm now we know is for each is funny it would experience an additional forests are pass to the direction of motion and proportional the velocity viscous forces depend on the velocity the viscous forests on a thing at rest there is no viscous for something arrest it's only moving the experiences the forest experience of the viscous force opposite to the direction of motion that to see that you have to see that that fits with this equation over here just shift pistol righthand side and it becomes minus H fight got so the forces along the negative direction relative velocity service force but builders base Our with viscous cool and that become invisible the viscous coefficient proportional age of freeagent case now in this particular case if does depend on time it would be as Zelda viscosity depended on but really interested in situations where the viscosity always H does not depend very much on our guard the discuss any of our honey depend on I'm sure in the summer it's less viscous in the winter it's more discus so that you could think of viscosity depending upon the perfect that's OK now for the moment let's suppose that the viscosity did not depend on time and watch what happens is beginning the viscous from the beginning I mean if we drop from rest if we drop the stone from rests in the beginning there is no viscous force because the rest and so initially it's just by double . be cause the find accelerates the evil larceny starts the increase according to Newton's law but as the velocity increases the velocity increases of becomes more important eventually will get to a point where this Karim matches and when that happens it stops accelerating which is right and performed by double . is equal for external force at minus the viscous drag on the viscous drag it's up to be big enough so that it matches half the acceleration stops that doesn't mean the velocity stopped Bernini object comes to rest it just falls but Terminal velocity through year term of Australia's final velocity reaches the point where the forests and the viscous force balance I'd so you calculate calculate beyond the velocity of Terminal velocity and it's going to be a threat of find got I won't put another symbol and this is the Terminal velocity all of the larceny that the cheese at the point where viscosity balances force that's equal to 0 provided by 3 h beggars custody the slaughter Terminal velocity so if we viscosity is very strong terminal velocity will be very slow and the song orders moved very slowly through the viscous fluid it is a case has really moving slowly is very likely that fight . will be very small compared to 5 of its Baroque formed through a really viscous staff stone then no other Connecticut Energy is generally negligible compared to the potential and keep them mind combat but that that's those are the equations of a scalar field in the the cosmological background cosmological context OK any other questions about but yes place in the last 4 years of war yes we aren't here this we go back the discussions of field theory any grungy descriptions of field theory which is some quarter among we talked but you don't want to ever think about the Lagrangian is just take it is a fact that the timedependent Sunni energy here introduces the viscosity 90 might ask what happened to energy conservation viscosity object moving to a viscous fluid but suppose for a moment that there was no force
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is just need you give a push to Connie know what happens to it slows down and comes to rest 1 haven't energy conservation well in the case of real genuine honey we know what happens if pizza honey there but there was no honey here was just the the equations of motion of a scalar field Illinois molecules to get heated up anything and so we should ask well isn't this Ghana sort energy out of the system yes it is but why OK them why isn't the energy conserved was mathematical system with grant you looks like since because energy conservation is a consequence of kind translation and this'll go Mangione with 8 timedependent is no longer time translation area and there is no energy conservation for equation for around you're right there just isn't any solved not surprisingly that shows up as some sort of turned the equation which mimics a mechanism which allows energy to be lost by the OK how we are all happy now this is want of the story Our the equations for an expanding universe in the presence of a scalar field only expansion affects the equation emulsion of viscous terms but now I can ask how 580 FXT expansion In fact what does it do to the expansion solo for that purpose let's go back to the cosmological equations the field equations the equations that as Friedman equation I'm going simplified just take the flat space case you could put back the curvature of you like it will make no difference what we're doing because it is small by comparison with things were going to keep our sorrow for let's right down the Friedman equation Freeman equation is a dark Over a square which we can call a square this is really an equation that each the 8 . 0 collision several a DoD already squares and that is equal to 0 8 5 G all afraid a pudgy over 3 times the energy density times the energy density times a week called role in the past but we now have an expression for role periods of faith in the square bracket that would make you make you lose the volume the energy density is fight that squared over 2 hours of farright so but that India but Oprah but but but but but the pride GE 3 and then took turns a fight that squared fall with 2 paucity of fight but with a day's worth of how assume why soon would prove it now we can't prove it but what assume some something which were a comeback tour From continuity equations now comeback the motivation for them and for while Our I probably would have started with the motivation are at best the question you got me going sources or you're wearing combat motivation let's assume that the potential energy is a where In a fairly large some units whatever units only a progrowth larger Nunavut Internet I love thee is fairly large but vary shallow potential the potential energy is gradual gradually deep and drawing its servitude decreases often misdirection it if it was tilted the other way we would simply change the definition of 5 so that a change signed a 5 and then redraw observer was tilted right tilted down the right until the end of the right with very moderate but yes legislator with 5 a series of your name for it you that gets them I'm glad that your readers Kobe and for a time has been discovered yet only indirectly it exist probably not but all scalar fields have to do with energy density in every field has to do with energy density period every field will contribute to energy density so every field has energy density but this 1 has as particularly cooked up to her to do Lewis John Paul as plus goes on view scalar fields were always balls are you plenty of very bars are could be like this 1 is tailored to do a certain job and a job that others scalar fields would not do because they just don't have the right properties Higgs field being particularly our doesn't have the right property and particularly its potential as much shallower like this and the energy density associated with exciting the Higgs field is not very high we want much more energy density there but there were works so far this is hypothetical description of the universe is expanding without with field fight that has a certain property rights of the field fine has a very gradual tilt to it they didn't fly a finger Pfizer falling now falling the right things always fall in the direction of decreasing potential energy Pfizer vertical axis I wanted you think of the things falling from space vertically but always falls toward the direction of a deep of decreasing go the depend Georgia in this case that means for them here now if it killed does gradual it means the forces small will come back chill factory have an equation here for H which will come back to a moment our but whatever age is it's not Zero simply because the righthand side is 0 particularly as redefined year so H is not necessarily small and the context that we're going to be thinking about the travel large later large big viscosity big viscous coefficient very gradual field 0 fix honey with a weak Forest pulling you down what happens you move you very quickly get via the
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terminal velocity of forces small features big The Terminal velocity is small and this ball which is really the value of the field gradually gradually gradually creeps down the hill creeps Creek very slowly so slowly that the fight that squared term here checked out we can we can we can we can use the Terminal velocity formula he could tell us what 5 . is approx. and then check that the parameters were with choosing for parameters are such that this is much smaller than that but what we've done that then high approximation as long as it's more rigorous slowly age squared off again saying equation H squared which equals 8 a square is mostly just equal pay 8 pie geometry and via 5 and moreover V R 5 is not very very quickly fired is very very slowly and VU 5 the height of the potential is bearing with time very slowly another words go pretty good approximation the feel the standing still and the value of the potential energy here is just whatever it is on his number approximately just a fixed number so let's keep Darrin Murray services at how does Lewis expand the movie circumstances well let's assume that because veal fight is so slowly varying that as a 1st shot at it we could just say that age is constant constant over a range of time until all those things flights appreciably different height as long as the rock up here is maintaining its at its height the potential energy we gives just V is a constant and let us do we get them and that case of course a constant what's me a solution of the equations of cosmology were constant age member exponential increase exponential expansion white 8 . 0 8 egos a Each 8 . lady a pickles each turned a solution of bad equation is an exponential expansion prime derivative proportional to the same object for the constant coefficient approximately cars constant coefficients expands by constant times eatery H T would have a beach resort each Webster solve this equation 8 they got over a year and ages each is equal to the square root of 8 by G over 3 kinds of potential energy on this ramp for the square socially we know side of the ramp costly my wanna fit the 6th to experiment if we CD if we were at retirement which this was taking place we could monitor how fast the universe was expanding blew it simply fit veto observation but things are interested in here are taking place in the very early universe which 1st to clear this is a theory of the very early universe of theory of the inflationary early starting point of view at that time v was believed to be rather large orange In any kind of sensible units which means that the universe was was was formed as a correct theory the universe world's exponentially expanding wears exponentially expanding with a large coefficient how large well roughly the guess the guests that a wouldbe natural cosmology would be the the doubling size of of the universe was kind of a minus 32 seconds but rarely got really accelerating really expanding at that time is not the theory of the current accelerating universe theory on the earlier will describe what happened later in a little while but this is the year this is the exponential expansion during inflation wrapped up front right next to large value of radio Ed Bradley expect any others seem to be out 5 more slowly its finest moving slowly because it's moving slowly the potential energy stays more or less constant with the potential energy which is driving the expansion of the universe its derivative of a potential which is driving fight to move but it's a potential energy itself which is driving accelerate quite different things right it is it's not 80 which is experiencing discusses flight so there's no drag on the expansion of the universe of solid going on here the viscous drag is on me evolution of the field which is keeping it pretty constant price why should we be interested if theory which the universe was expanding very rapidly from possibly some significant length of time time now being measured in units of 10 to the minus 32 seconds after wife should we be interested in such a hearing the original guests about this which went back down rules 19 80 did not seem terribly compelling and yet because modest caught on to it very quickly because knowledge is theoretical physicist by now it has been confirmed but it's 1 of the year 1 of the stories of the theoretical physics and guessing over the guests was a kind way gas the puzzle with 2 puzzles that this was addressing it was similar puzzles fact do you are related to each other but the 1st puzzle had do with particles called magnetic monopoles now None of this inflation has ever been discovered yet we assert take that back this inflation is now by now welcome firms inflation being experiment this exponential expansion after we know that that really did happen this we know with some degree of confidence that really happened on and happened long enough it happened long enough that this exponential expansion cause the universe to expand by at least each of the 60 all our expansion at least we know that move a comfortable how but but yet OK so that so why should 1 be interested in stretching the universe universal much 1st reason was apples monopoles a once again
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said particles that have not been discovered why introduced 1 crazy theory with public and discovered field to worry about particles which are also on discover what was it will always trying be explained not the fact that you didn't see the wealthiest effect did CEOs particles of arms but not a prophylactic those particles were discovered yes I take it back to try to explain the fact that those particles were undiscovered and that that they were discovered by particle physics experiments namely that they weren't just for now appearing universe and the way I think there's a magnetic monopole limit restore magnetic monopole isn't what it would be expectation for their properties here's a magnetic monopole plays the same role with respect the magnetic field as an electric charge plays with respect to like it's simply a source of point source approximately point source of magnetic field with magnetic field radiating out from it and call long pattern exactly we have a lot of electric magnetic monopoles according the current theories have never been discovered in a laboratory because they're very hairy how heavy some lawyers up near the plant grants that's could put all Nutshell magnetic monopoles are believed to exist they exist in most unified theories I would say they exist in every new unified theory that we can think of our and In most theories very heavy heavy by comparison with ordinary particles the fact that they are very heavy perhaps 19 orders of magnitude heavier than the proton would easily account for the fact that they've never been seen in the laboratory OK but now let's go back the very early universe remember nearly in the universe was hot and when it was hung off it was enough Connecticut energy in the form of both kinds of other particles that you didn't need an accelerator To make elementary particles at 1 point the temperature was high enough that their fault times would the would scatter off each other and produce electronpositron pairs earlier was hot enough that photons would scatter of each other and produced protons and hint that protons whether goal a way back to what physicists thought was the very very beginning the temperature according to theory was how enough that it could have created magnetic monopoles pairs of them just like you create pairs of electrons electrons and positrons temperature was a 26 orders of magnitude higher than Sumpter than temperature for electronpositron pairs it should monopoles now you you can sir yourself what was your case this is wild wild speculation nevertheless every theory that we know about seeing the contained use monopoles where were the 1st of all monopolist can't easily disappear they have they have a charge they can't just disappear what can they disappeared into they can become electrons and protons and other things because electrons and photons of other things don't have a magnetic charge magnetic charge would be conserved just like electric charge so these particles on they annihilated in 1 can estimate how likely it is that they all annihilated not likely pass the course of the universe as it evolved we would have expected to find some population of magnetic monopoles floating around the space maybe not very large density of the universe expanded a lot since the kind of coupling expanded by a factor of thousands of the time there was high enough to create polls according to the standard theory it would expand a lot more than that Soros they would be pretty dire look but they don't seem to be there I no wonder why they don't seem to be there they would have been interesting effect on the magnetic fields of galaxies if it were charged particles around what happens if there's is a big an electric field around and you have a population of electrically charged particles and particles they discharge the field a bunch of particles ladder if you have a capacitor creating electric field across here and in here and there was electrons and positrons plus charges in minus structures plus charges structure the plus by the capacitor to the minus 1 happens the plus side of the capacitor pulls over the negative charge that about my this side of the capacitor pose over a positive charge and in discharges the field discharges field in the same way as the population among the polls was as large as theorists estimated and if they live lived forever and they sat there In the magnetic fields of galaxies over the period of the age of the universe they would have discharged year of the magnetic fields of galaxy magnetic fields of galaxies have not been discharged that there exist so it became pretty clear that there's no significant population of monopoles out there even the vote the standard theories of the Times in 1980 and so forth predicts Stanley cosmological theories predicted that the universe was hot enough to create them and in the process of expansion did not completely dilute them away that was once argued that was 1 set of facts the other set of facts was a homogeneous of the universe not today's homered unity but the Hong virginity at the time of the deep cup having also homogeneous stand by looking at the cosmic microwave background in different directions a space as time went on the temperature of the microwave background became better and better measures and was measured in different directions the flocks of radiation coming in as well as the temperature of the distribution were measured very very high precision all over the sky and found that it was meant to look please almost absolutely at the time and 1980 was absolutely uniform the 1 oneparty minus for something like that 1 part of a 10 thousand or better it was absolutely uniform sky and that is another question raised the question Hawaii is everything so 1 at that time was everything so darn smooth and no standard theory of cosmology could explain start with a small universe very very hot likely they have all kinds of fluctuations in and the bumps and lumps what end expansion from From a standard expansion would not have flattened about smooth to the degree that was known to be smooth and homogeneous the guessed that that ghost made it was very very early and monopoles have been produced in a after perhaps the universe have a highly complicated texture and the
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northerners amount of expansion came in died eluded the mock polls so that enough expansion will die loot anything serve that the survey year presence of monopoles was just alluded to to the point where there were many many fewer of them there had been estimated and it also by loaded textural lumps and bumps that 1 nite expected to be the nominee could prove that they wanted that you could just say well you assist started very very smooth the states more you could also said the universe started with not polls but there was no good reason for it with 1 shot the idea and a very very early extremely large amount of expansion consult both problem flattened everything our a smooth out just like a blowing up balloons along its move and loot twoyear density of these my samples was estimated the estimates vary to some degree but was estimated that if you want to make these vs. and flat as it is from unknown starting point the or unknown starting point but except that the unknown starting point is not terribly smooth if you want to start with something which is not to smooth and blow up which presents smoothness you have that colds approximately 60 East holdings 64 things and Eve folding is a multiplication by be used 2 . 7 earned you in order to our arrange the facts to be consistent with the known flatness you needed approximately 60 new folding or a factor of each of the 60 which means that is he he had to to be at least 60 that in itself tells us that there's a ramp mustard and radish shallow universe had to stay on the ramp for a sufficiently long time for it to grown by factories 60 it doesn't tell you any details as all sorts of ways you can but you could change 1 thing in change you have a thing but the working numbers is that there have to be eaten the 60 or 60 Newfolden of inflation in order to simultaneously account of the lack of monopoles turned relax structures in the universe at the very earliest young would there is no reason why it could not be completely chaotic that no no 60 60 would be enough to start with something which was very chaotic and rough and stretched out on the not of get orchids maybe was 70 but but sexy of the minimum 60 is the minimum with with you make your assumptions worse you need more the hold that gives it's only telling you that there were at least 60 now you say that the universe at the very beginning fairly rough but not very rough forget about 60 years there was rougher than that from 7 to say it was more texture than that becomes a minimum minimum number of beef all things is 60 now again these numbers are not hard and fast by changing the Syrian this way this way you could probably be about 40 or 50 but 1 that 1 doesn't uh room Ferrer pushing numbers around a little bit but I would say with reasonable confidence we know that the inflation took place so as to expand the universe of money to the 60 50 or more and upper bound we don't have could have been eaten iii Veguita the the then the center tend to a 60 yes it could have been nothing in the observation tells us 1 way or the other arm that would be very remarkable because to do that you would have to make this extremely shallow near defined tool used the shallowness of it and so forth but still there is no no after bound it was a lot that law bound of about 64 holdings that votes necessary to understand flat so for OK so that's that's where things wide 19 Alan booths postulated that but this exponential expansion in order to drive the exponential expansion be postulated exactly a potential which looks something like this the 1st round of theories was not quite right it got it got into the former describing now after a euro to underlined a year over people so straight out but that I wanna go back to much of the history because some of the history was wrong nuts history was wrong the physics of our but ultimately it got straightened out aware of the theory look pretty much like this a shallow ramp which supported this inflationary tendency for at least 60 folding now 1 interesting thing is if he is the number for things would just barely 60 Bellarmine new army of being able to see exactly what it is that inflation was invented to get rid of right Fletcher was invented to get rid of something this is how much you needed a flat amid the current flight PARIS what a full ride on the pitch before arriving on that it means you should be on the threshold of In the next round of experiments being able to seize some additional curvature of the universe so 1 of the things that will be hunted for my year about satellite and other rounds over a observational cosmology will be to see if the universe really is flat might have curvature of spatial curvature might have positive curvature might have negative curvature and the fact is inflation does not tell us whether there was more EU folding and 60 adjust color still had to been 60 in order to account for the present data always in such circumstances it means that you have a chance to mix around our effort if you're on the air if you're age so that this will come to watch this this allimportant it is important young that later that rap start young my right there was a it was right so the 1st impression which is close to the truth is rapid expansion called the universe cooled the universe expansion cool things and darned if it was just classical physics which is classical physics and you have some
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heat in there a box Newark's exponentially expand the box very quickly it will cool Truro negligible temperatures so the 1st entered is at least a classical universe this rapid expansion were called it now so 1st dose 1st statement births is there was cold very cold during its inflation during this period he recalled because he capital of dialog everything got the space was dealers expanding rapidly it was empty of all kinds of structures empty in the sense that looted art would particles or I die looted monopoles will die looted everything else was there were empty as health and cold OK now was promote the want forever why not no theoretical reasons 5 this potential have some other shape it your mom richer longer but we know it arbitrary here the uterus is not doubling once every 10 minutes 32 seconds so something happened the natural gas is that this potential did something different it had a plaque told came to the end of but why it had let why it had play and 1 maybe in the plateau looks like theirs is a mystery today we don't know what we know is that this is a pretty good representation of cosmological data and about they were about the bottom here bottom represents today the potential energy of the field is very small from back for a while as of this is your model if this is the model that works Howard's work 1st question is how the universe get here in the 1st place not part of the initial conditions 5 of course initial conditions in this context means that's how far you could trace back there with anything like observational data so we know from observation data CMB data and so forth the deal was a period of inflation must started appearance on point how we got here we do not know what's around a completely arbitrary thinker starters and it requires a theory requires a of some cosmological of setting the say why we see really start he do we really start he we come down from some other place but tracing back as far as we can go it looks like a good bet that we started somehow like this and gradually gradually gradually rolled down this hill taking long enough that 60 fold but it was placed in a career in Malaysia he is also much before March before if your much before not but before that right now what happens when you get to the end of this book when you get to the end of this but steep enough viscosity becomes less important 1st of all viscosity becomes less important for 2 reasons as you go down the hill here H. gets smaller what age was each is proportional to the square root of the energy of the potential energy of the potential energy gets smaller remember beach gets more on the other hand death Forest gets bigger as you down the hill year sold viscosity becomes less important force becomes more important and they expect the result is that you would benefit slide down words weren't you got to be edge here your slide down relatively quickly inflation would stop and the process of sliding down the hill here energy was released potential energy the potential energy of the field disappeared its throwing expanding universe that energy is not strictly conserved but even then an expanding universe this summer memory of it's not expanding too fast you still don't get to use at least approximately energy conservation of this potential energy suddenly disappeared it will be made up for by Connecticut by something so it's thought that as you would over the hill here the potential energy V that converted to something else while 1 thing that we did converted to is the velocity of the field obviously but then eventually you get down near the bar when you get down to the bottom what's assumed there was a bottom and you get stuck at the bottom is the energy the energy somehow got converted particles From retain heat at some point all of this energy appear that converted to heal that's that's was for the energy get converted to heat and that at that point that's where we usually start called the Big Bang 1 his vast amount of potential energy which is believed to have been a very large amount of potential energy suddenly got released fairly suddenly that converted to heat and that he was the starting temperature of the year universe what began as a hot they are a big bang of Big Bang has to do with what happened was slowed down here as a down there lots of heat was generated he goes generated replaced the righthand side of this equation by perhaps radiation nominations and that's the period when the award stand because myology started as you Obama's Hillier young pace and less Is that both did yup yup yup 1st right exactly what I said when I say exactly that 1 thing that that's 1 nice serious 1 nice way that could've happened on In on field it is itself a field that has quite that was quite called in for In August partners if they would be called in for and so as a rolled down he said I don't think of the field is increasing all you could think of it as the production of lots of info on articles if found particles themselves were unstable they could be Caliente electrons positrons 4 times other things and that would be 1 explanation of how always energy that converted to heat then particles so yes that that is 1 noon story which some form was probably the right story by the time they were placed well solid base be guns with the start with some wears down here on the slide down here is wary the Big Bang that we normally think of as the Big Bang began a hot
1:09:33
pink then now what is said because the clear How they entered into space that existed that a huge amount the space was created by the inflation as for the inflation data is it bull up this fictitious well we could not sure exactly where creating space means but let's suppose what it means is makes place bigger will not stand starting point but let's take as a starting point some need a 20 year of 3 sphere of space and wanted everything else were would mean by saying creating space we we made it bigger we made a bigger to be a will around have stars and galaxies and so forth have interesting spatial relations call triangles and things of that nature and that's simply involved expanding the uterus by a factor of what each of the 60 would be about 10 25 or something Kendall 26 26 orders of magnitude of expansion is where the space was created after the space was created it was and it was empty wrote that where was full of potential energy say was empty is not quite right it was full of potential energy of the potential energy was actually the form roughly speaking at that kind of dark energy except that was of a much much larger value In today's dark energy it was potential energy was a potential energy of the field that got eliminated when roll down the hill something had to replace it were replaced it according to period was was particles heat light and all the stuff that the universe began will begin with In the sense of standard cosmology OK Arroyo banter about what about the bottom was there any potential energy left over at the bottom of yacht and accord today dark energy right the uterus is still believed to be To be expanding exponentially but without tying Hubble constant not once every 10 to 30 per cent of the minus 32 seconds but wants every year a 10 billion years that requires I'm very very small potential energy here that's what we today quote cosmological constant yacht I thought I had sex the following the mom Pulver battle it out of existence during the 1st round of doing it but I don't think 1 readjusting my report on the edges Cincom curvature I I don't think there's any chance of seeing multiples we know that these are galactic magnetic fields were not on 1 but the precision with which we can say anything about monopoles from the fact that the magnetic field was not on 1 was not very good we can do is measure the curvature of space the curvature of space has been measured to some precision is less than 1 per cent in some some units and next round they will go down possibly toward was magnitude knowing they discover the spaces Kerr learned most of Titus constraint on here is the fact that space looks flat roars was enough inflation that flattened things out to a degree where we ate at present cannot measure any curvature prospectus it's got to be part of it is not until their that's the rectum state energy of today he now why so In some senses and nice unified picture of inflation and dark energy on the other hand it's a complete mystery why the number down here a hundred men in their 20 orders of magnitude more than I was up here that's part of the mystery why this drawing on the blackboard is if you could see this but on the scale of drawn here it should be a 120 was magnitude smaller against that of course the mystery of the small cosmological crimes cell which is where they gave the order for 3 days they have that led is moving up close them their Dumitru occurred of a that I can say is that normally create all you're in trouble if the mock polls created later wrong you have to juggle the time scales here to make sure our the time and energy in skin skills and so forth on right good the question is when it fell off here How did he universe did heated up plant temperature in which case you were back exactly where you started plenty of energy to create samples or if he did something more moderate than markets that depends on the details yes you're prevail you're right that is a question here this this is called reheating incidentally why it's called reheating and not just heating I don't know but it was car reheating and reheating took place and created a certain temperature is essential at that temperatures low enough that it be below the threshold for creating my appalled otherwise you back where you started monopoles were created on this leg of the journey over here your back so so those over there had been 1 days is before they say they may have existed before expansion happened would they may have or they may have failed To produced for the simple reason that was not enough now you have to Joel numbers to store down but a numbers are crazy so what but but we're down the bottom of a truck is is expected not only no our Arab it but the reason that doesn't shooters because of the 1st version was not from all of assess the shot we'll now now this is a parameterization that fits observation we don't know why I was so flat here now we don't know why I couldn't continue before there's not theory but those those less say there is a real estate cause for let's put it this way I think we only
1:18:09
end any of these questions the only when I sing only answer I don't mean to say that it's known to be right and only answer around is anthropic Blair the universe may be extremely begin may have many many many different environments of all different kinds and you can ask you we are what did it take what kind of environment was necessary for us to exist now the thing is a lot of this is necessary for us to exist of certainly we couldn't exist of the universe 0 as big as a peanut or had 2 of evolved expanded on highend that I didn't want to get into that tonight but the not structure of the curve is dictated not only from from observation but most of it in large parts of it are necessary for the universe 2 of involved something that looks like what we live in a somber comeback for that but other than that we have no explanation of why the features of the curve that we don't know are they and he's there this there a hat call hero as a a major loss is seeded 1st time but there were no loss life runner is just a bit of up and the example of something the matter or I was like 5 5 or 6 days well to way you put the 0 0 5 is completely arbitrary where you decide of setting fires equal 0 but here you go here but here it might like to put year where it is today say that's 0 5 the figures today about that there's a bit of a final monograph a weaker mark off times misses our pendulum minus 32 seconds sources but tend to minus 32 seconds 10 miners twice minus 32 seconds above our is 60 times tend America's 32 seconds at Wikipedia but certainly here 60 times they have doubled or what they have multiplied by E. every 10 to minus 32 seconds then in those units by the time I went over the edge over at least 60 units of he holdings maybe more so find ticked off here and they relatively quickly he went down the hill here How long will it take to go down the hill probably more than 10 to the minus 32 seconds probably a lot more bar star on the scale of ordinary time pretty quick he the energy a back hell of a ride says came back with shameful that that is is not here all Work yes that's correct it cannot go back up remember that the equations of cosmology have any friction tournament the expansion of the universe today is big enough to provide a friction that would make it very unlikely for this tour through spontaneously corporate right you're sitting in a year or more another way of saying it is it was the friction turned the broad arrest them they've were shot me of maybe even wrong a couple of times but Of the friction turned due to the expansion of the universe were of slowed down will come to rest and then just like any kind of object in this Castillo's a rock sitting at the bottom of the sea is not going to suddenly spontaneously our command With the idea of a series temperature yacht the temperature was very cold during this period he and then during this period hero and particles with dumped into it we don't know with any detail what the temperature was that it was heated to by the time cut them here but we do know is that had to have been hard enough to create gold particles or we know and love Court of everything else so it had to be in the year in the range of a huge particle physics temperatures but there are priority workers at wrote temperatures of 40 of the electron volt does room temperature we're talking about temperatures which were high enough to create proton and by proton Parizeau pub very likely much much harder than that of 40th of the electron volts from room temperature that's 300 degrees a billion electron volts to create proton that protons there's but a billion times of times while 300 times warmer 40 so where it and the 11th and 12th degrees something like that was truly degrees or higher on that's probably on the very very low remember you have to have heeded the universe up enough to among other things you had universe up enough To create the barrier on except to create a proponent by proton pairs of that sort of thing but probably much farther Storm is not yes yes yes woes on the court yes yes there are they arm on the way down here they decay in the process of became produced the usual particles but that was saying questioner was history of HBO's arms Osborne's arms detainee 5 and the border they decay tool photons electrons quarks a anything we create ordinary energy density and dark matter for that matter probably more dark matter than anything else on your list a set of fresh both decrease is but you just outside the city that I thought I might add to what you do is say at that time there saying it sure looks like it so far deaths in an East Asian leaders that a military arms 1st right at the present time that's right at the present time looks like was stuck at the million ends up on West something else happens that that is not built into the equations at the moment are will stay there forever no 1 existing does what happens if we stay there forever if we stay there 1st of the universe exponentially expands now it's true it doesn't exponentially expanded rapidly but still every 10 billion years of doubles by it takes how many times over a trillion years through expand us so much that basically the galaxies will have all receded from each other be moving away from each other outside the horizon we will our galaxy will be all along there will be a well drama might but then they drowned probably will merged with our galaxy everything else is
1:27:35
mulling a apart and we will truly be alone out there will be nothing else but brought the Milky Way and v cosmic microwave background of cold to a temperature which is way below detectable Everything else in between galaxies will have stretched out and their looted 2 point not play inflation current inflation which is taking place there is low inflation and a few trillion years having a good deal less than that of a different about it but a few trillion years there are Galaxy will be absolutely isolated and a physicist who live on at that will have no way of knowing that their product a population of large numbers of galaxies they will not be able to measure anything about astronomy they will not even be able to tell but there are undergoing a year and accelerated expansion remember how did we discover the current dark energy we discovered by astronomy we discovered by looking at the c and b the CMB cosmic microwave background it will cooled to a temperature which makes an undetectable everything in astronomy will have a departed in Ghana now through the horizon and so we won't be able not we but they will not be be able to tell that they're in a inflating accelerating universe if they come on the scene without history books and sell for at least for some period of time the imagine what before some period of time the look around and universe which is 15 billion light years big they won't see anything they won't able a callous 50 billion light years ago maybe send out probes in the probes will go out there a fewer thousand light years and come back from I saw nothing was nothing out there and they will discover themselves a unique phenomena sitting at the center were of course call Salzar center and the 1 and only 1 such things and they will be puzzled there it will be possible and then some smart young guys come along say Hey know maybe they're a lot more out there but maybe the universe just a lot in and they just went away it it is clear that what won't sources you know what it is do you see that In 1 . 8 based Gagnoa knowing but of a bed of his bill if there's no space but only this tiny little nugget overtures what is it a point source in you're imagining that this thing is in some of the space but that's the wrong idea about how they want you have somebody else said years down 0 4 we can see our yes but there yes it will be analogous except that everything apart from our own galaxy will be out beyond that point ready that get galaxy might be able to detect old transmissions of Groucho Marx that I don't think so they will be red shifted did to the point that there will be no but Barbara fondue its purpose rebuttal 40 who had a long time to get the job it is a question that ominous thought this the sweep across a case where you guys that question can question my a yellow OK no no no there is no the U.S. massively in on particle has to do with the curvature of this here and we know nothing about me nothing about all of the other thing we know is it's not so light that we would have produced at accelerators that's about all we're where we were going sweep across were to broker is a sign that the whole absolutely a yacht our again and again fired might have started with lots of ripples but In the process of this inflation taking place those ripples got stretched out so a after a couple of evil things the rebels would have been known you know pretty much eliminated locally and you could forget them all work on backtoback interprets down this time does not with swords quantum fluctuations we will come back to for the moment let's just imagine classical waveform and get stretched out that's the primary mean things that happened superimposed on top of that will quantum fluctuations and they will play an enormously bigger role when we come back that way because steps Corymbia Asturias through broker combat your broker your your your your next also generally today's leasing gas is slipping over the on the horizons so red shifted all we see out there is cosmic microwave background we look back that far 1st of all we seen universe that a derelict time before galaxies forms were look way out there and the furthest because he is to surface of decoupling of surfers were or services West scattering but that that means the place where the universe were opaque a pretty much out the year the year of Verizon we see further than that we could we will be looking back so early that they would have been no galaxies there Serbia should know we can't the only at a later time then look over the however seems for problem look out for you always see pretty much the same thing S it makes very worried that it's easy for you to us they get us teachers salaries be well armed weather will have as the observation we thought we were they will have still exist stars to exist himself for what they will have their little galaxy and there otherwise completely empty spaces very hard to to see how they could do it any observations which would directly tell them that they were in a space which was inflating once every 10 billion years or 20 billion years I can't offer he and think of anything they could do with short on sending howled probes which would take of water billions of years to go out there and come back and make measurements on home global structure of the universe short of that I can't see how they could tell us what the expansion properties of the universe were anything else they could do that they could take tens of billions of years and explore but they Kinkel too far because of the go father go outside the horizon they take it back they can only go on distances of 30 billion light years something like that 20 billion light years sends signals back and forth which will take billions and billions of years triangulate discover the fact that things are received the receding away from each other but before they go too far come back so in principle they can do geometric measurements discover this curvature of spacetime discover the fact that there's a dark energy arms but it would take billions of years at least with the level of of precision think with better levels of precision they would have trouble as
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a astronomers anything like our astronomers it will take billions of years there reconstruct factor period waiting universe he gets the best he can do that they can see there are still is a close game here I have come back yet I actually want as some observational cosmology is a really true that or what will see will be arson in drama and I think it is true or think everything else is participating in the outward flow enough that they will they will receive our bird Europe young exult a 3rd set word that mci's at the give us a lot if there firstly is a function of our Wide World War II write equation Michael Ryan equation started here slowly drifted to the right suddenly picked up and went on to you but on a linear up here gradually linearly tracking along here will adapted here became OK yah you're free to submit bill way in the future exercise actually central said that he their energy should say should take at some point where we've that can they must not go there must not go past the horizons of both the king the back which gets smaller but bacon subtly go a few billion light years out in combat and that should be enough for them to be of a measure carefully properties How much is 1 remember a few of them sending light signals back and forth which themselves would take billions of years to travel Baker probably do some triangular addition have thought about what's urgent thing on my yah yah so it is no not horizon will stay out there are roughly 50 60 billion light years ago the remember exactly what it is but a man is just say this is not a place where spaced not less stuff is same space there is a lot of space but not much stuff has friend Ballengee where the recession velocity the galaxy approaches we'll just north of the 3rd year sitting here the potential energy is constant and the Hubble constant is constant constant Hubble constant means universe is expanding this way or ordered also means that distant our velocity is equal distance and Hubble and Hubble is constant now so you cannot solve the equations and what distance away from us things receding with the speed of light and find distance divided by hobble sorry see divided by hobbled is equal to distance what you'll find will be of water over of 15 billion light years right from the numbers 15 billion light years and that's where the horizon is that things are receding away from us with the speed of light OK I get what the structure seems to avert the very provocative both are down are about a foot did it out with your arrester galactic show I mean Of I think sell somewhat but not a lot now I know think it's a good thing it's going on family stars there will be what density of stars don't know but I think that will survive protruding ears and I believe I I never I never was sufficiently interested to track down NASCAR my friends were details are but I think they will still be the Galaxy will still be stars survey lock bills will be planets intelligent creatures on a states that those changes businesses over the years a that to some extent you could imagine there goes energy were stored in car condensation for Toms there was released as came down here and media in 4 pounds to Kate that again I mean much of aren't telling you would have to be truly in order to explain why a humorous is and was the way I was during the observable period we don't we do not understand with any great the mark inside y if it is the picture but we do have significant evidence now that that is work picture was your perfect I we have 15 minutes or so the next thing on our agenda is to understand after all this inflation y Is isn't the universe completely small the amount of inflation that took place in order to make it flat in it would have made it so smooth that they would be no explanation of the structures that are out there be inhomogeneous that's out there there so the next thing we wanna come to is the fact that the universe is not homogeneous and it has all kinds of structure on various scales ever tell you a little bit about that structure and just a very naive our but still more or less right explanation of why the structure appears the way that it does not not talking about and order traces back to when I say the structure I don't mean galaxies galaxies small potatoes on a small scale I mean a much bigger scale matches clusters of galaxies provoked supra clusters of Super clusters of galaxies and they formed a structures that fills the universe that does have structure does have structures not completely homogeneous on scales and that structures quite fascinating and I think largely understood but it's mostly understood by simulation the simulations start by assuming universe was not precisely smooth start with a certain pattern of non smoothness call the fluctuation spectrum which of them study it and they allow 0 gravity and just the motion of objects and so forth To involved and see that creates structure on the biggest scales biggest scales of super Dupre clusters of galaxies on gravity is not all that important these on scale of our galaxy are certainly the scale of a star a planet gravity is with cold things together on this this structure that seemed that is largely nut summits and not coming from gravity and would be there even if there was no gravity but what it takes to start
1:46:28
with them in a home originated some fluctuations based garnered so I thought I would talk a little bit about the theory of how structure that formed the theory that show you is extremely simple extremely I gave you 3 pictures talk that would be a hazard but is seen the 3 pictures I send them to you by email farright picture No. 1 it is actual for a graph of the sky but deep deep deep astronomy billions of lightyears out higher rates shifts and what you see is patterns of light which has some structure to its not feature end of my couldn't find his good pictures I wanted but what you see has a kind of filament restructure are you could see it on the pictures but there are better pictures I couldn't find the right 1 I was looking for kind film entry structure of these filaments I'm not single galaxies that thousands and thousands maybe millions of galaxies huge number of them forming a filament tree structures in the elementary structures intersect and former complicated web at least photographic William sky and that Web so this is on this is an an exaggeration because the pictures amount that good but might look something or that at the intersection of the filaments things a particularly bright again these are not single galaxies particularly bright at the intersections of them big voids in between and the filaments their parents elements and that's the rougher picture on scales much much bigger than a galaxy that them bigger these cells are OK Oracle look up next 2nd picture picture 1 sky real thing picture I will not be because it looks the same picture tool is simulations made by people what they do they start with a bunch of particles the galaxies produced budget particles with some kind of spectrum of fluctuations fluctuations means a little bit of randomness in India velocity distribution in particular the 1 region a space they might be moving a little more this way other regions a little bit moving this way traced back for some primordial variations which will want understand but that's where you start with a new let it evolved for a while start with you will form a good starting point for this would be a uniform distribution of stuff but with variations in velocity small variations the embossed the velocity variations which are the most important thing in what is say a after a time these simulations you see a picture which over here would look just like this except shopper clearer why because it's simulation and they're not looking through a telescope but billions of lightyears from the White years of the right use more for over a year and simulation with great detail what is left allow more movement None None right on a show you the theory that you would get the no forces and the last victory but not less pictures that's a beautiful blue Carla at the bottom of the ladder that life forms patterns at the the bottom of a swimming pool a war they look like they look like this exactly like you would have a hard time telling the bottom of a swimming pool from Merv simulations world the lack structure they look very very similar to reach of course wonders in 3 dimensions in that there's a big difference but of course we you see is only twodimensional resource import areas of EU Rio university and simulations of it have a remarkable similarity what's explanation of explains that this is something called cost cost 6 were 1st encounters an optical phenomena mainly the bottom of a swimming pool phenomenon and we can make a simple onedimensional version of it if the world a onedimensional cost 6 would just be spot of the world affairs the bottom of the summit was replaced by a oneday Mitchell bunkers pulled instead of seeing lines like this you just east spots of high intensity OK let's try to explain that what's what's good the explanation these caustic caustic soda spots of high intensity and in 2 dimensions the bottom of a swimming pool and replaced by network of knock spots but lines of highintensity ended 3 dimensions who find that were replaced by what's good for it lets suppose struck picture here time goes this way or the depth of the swimming pool that the depth below below the surface of plot debt vertically upward as because perversity the bottom of a swimming Pelosi of populism impose here is a top assuming 4 of the top of the swimming pool has some structure to it from the optical point of view will only Venus in the part of the war light rays come iand there refracted a little bit and so will you have a rough surface year and angle delight goes off different direction our will vary from place to place cellulite may go straight through here like they go off and angle here and they go off at a different angle over here and up again here McAuliffe here and over here for the pending come exaggerating its because this is an exaggeration is being doomed to the random fluctuations in the starting point of the light with the starting point of the light is is place were void comes into this room it at the bottom someplace and what you see you see these and the onedimensional case used see spots of highintensity that Celia explained that let's call me access are down here let's call X don't this week and I think our this picture as representing the light waves from the top of a pulled to the bottom of a pool or we could think of it public different way we could think of particles Starting with different velocities particle starting with different velocities at T equals 0 17 the couple were this would be sequel 0 and instead of different angles politely fracture through slightly different velocities as we move along OK so let's start down here but say it 0 let's think of it there from the point of view of particles moving so as seafood 0 let's assume the simplicity of the particles are uniformly distributed with no tendency the bunch up like this at all uniformly distributed but slightly different velocities as you move from place to place right so let's say that's fine b and might X is the number
1:55:55
of particles per unit X along with axes begin by the X small number of particles in the small X divided by D X is what you would call the density of particles from the factors which is good Take that B 1 we attended the B side anything we want our beverage just uniform feature lists the magnitude of it is not important what's important is featureless To now what happens to each particle let's call the position of the particle after retiring instead of calling it acts let's call it wiII appeals court 1 why of tea that's the position of a particle which lets say star didn't point X if the particles were not moving we would just say it wife of is equal tax the position of the particle after a certain time would be the same as the position of the particle when it started an X is just a label that labels where the particle lives with the particles were start that elusive particles both particles which moved in with velocity V E N V depends on it the velocity of the particles depends on X than we should here plus via of X punch feet the particle acts had velocity V of X and after a time see high it will have removed a distance VOX decals for me as a starting point the start of the point decks and after a time see it's no position is X was VOX times is that clear right now let's try computer at a later time comedy particles their aura per unit wife why is no cordon of the particles were interested in the density at a later time while we want to computer it by D 1 the number of particles per unit wiII at a later time but so what's attract the trick is differentiate this equation over here now with respect the kind but with respect to acts so we have Russia scholar Wii PYE by D X is equal to 1 plastered the river v e with respect to x what's called trying beat kind of X times and differentiated both sides of the equation with respect to X was annexed that anybody guests we have the MDX we have YDX what we want is Dione IDY the and ID X which is 1 of the X right but they explained why is just 1 over BY by BX so it for that end and by IDX is 1 yeah this factors as 1 divided by 1 plus veto prime of X and T Whittier 50 is a bright spots are after trying t yes it with the denominator was equal to 0 this is a density after time where is it on be big Of course in the geometrical optics approximation get something in there and the wave theory it's not really infinite we're going to get a bright spot especially bright spots at the places where 1 close V prime of vexed and he is is equal to 0 OK let's think about that was similar to figure out what that looks like armed now let's plot b Prime of X is a prime of X and if there is remembered varies was it average around for a good idea for that's average might be 0 was assumed 0 Soviet trial of X price of experts be primer Rex there's something that might of fluctuate as you go from 1 place to another in some places the particles of moving the right steps would be vapor sorry some places be promised positive in some places negative and when do we get in trouble in other words when does this thing become infinite it becomes infinite way when meet Prime of X times T minus that is equal the 1 OK but instead applying V prime I will prompt might be prime just because of this signs I told you this was a prime actually amid mistake it might be prime this is my be prime and he is 1 up here today after a small amount of time V current terms EU it is
2:02:12
not a primetime TV after a tiny amount of time small it's just shrink my idea of a small number tea and there's no place for pass 1 but now what happens is he starts to increase each time of X increases it just get it just gets a multiplied so after let's say his seconds it's now summer bigger U.S. reading is just times bigger than it was at 1 sector still no crossover points this is not intended to be periodic particularly its intended to be a moral more random than that but a accidently Jewish random tying keeps going on V trying times he keeps getting bigger eventually 1 of these points this 1 will get up on a year no war happens at that point what prime time stays has become equal to 1 the denominator has become 0 nominated becomes 0 that's where you get a lot of intensity that's where the intensity the number on intensity of the was light rays it would be intensity and its particles together Hulu German hands Man of the year of the particle density about point so only here an extra stronger density of particles are an extra strong density of light hitting the bottom of a pool then the rest of them are still down here somewhere you although further this point splits into 2 this 1 comes up there and eventually goes over the top of the ceiling here and creates more spots these are ah cost 60 so what cost places not cost it means the little meaning of the word Costigan sharp that's where used sure features these points calm along the bottom of the onedimensional swimming pool get is a very very sharp birth like spots now if you want to do exactly the same thing in 2 dimensions and we could work it out of our time tonight but he didn't 2 dimensions we start with the twodimensional world and particles moving upward twodimensional world being either a twodimensional world war the top of a swimming pool and you Ieave either and Heidi time what you see is basically this there are of course hotspots remember the amount Spottsville lying light and they intersect and you could see that about from import facts in the bottom was from pull you'll find extra brightness of the place where they intersect so you get a network of lines in spots where the highest intensity being at a spot highintensity along the lines and big void is now in this case in the swimming pools avoids of water devoid of light missing slide in 3 dimensions if you play exactly the same game now what saying we're starting with a 3 dimensional world with a uniform distribution of particles but velocity dispersion of the same kind what you'll get surfaces intersecting other surfaces their complicated form surfaces the caustic soda surface is the surfaces from time to time and place the place will intersect the long lines and the lines will intersect Long Point that saying when you look at these simulation you can't see the services because the surface of distance from viewing but you do see the lions and you do see the hot spots where lines intersect sticks so this is what you expect in a world without gravity no gravity is invoked always invoked was a distribution somewhat random distribution of very small velocities starting point that would hurt also have some variation of density along here those with it would make much difference are basically the same thing and dumb that's if you like a very simple but not wholly inaccurate weary of large very largescale structure caustic on scales course gravity plays a big role in courses things to convince the galaxies and so forth but the point is we the the the reason I emphasize this is because we have the have series of this variations in the initial velocity distribution and where did it come from we said that we stretch the universe How would the point where it's incredibly flattered uniformly where did this come from where this starting distribution of random variations in the but there are variations of velocity come from that in itself in in Homer inhomogeneous so next will study a little bit is quite the origin of the inhomogeneous but in no way in the universe How work with through restored imported for which the for more please
2:08:27
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Metadaten
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Titel  Cosmology  Lecture 9 
Serientitel  Lecture Collection  Cosmology 
Teil  9 
Anzahl der Teile  9 
Autor 
Susskind, Leonard

Lizenz 
CCNamensnennung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/15057 
Herausgeber  Stanford University 
Erscheinungsjahr  2013 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Physik 
Abstract  (March 11, 2013) Leonard Susskind presents the theory of cosmological inflation under which the early universe expanded exponentially before the Big Bang. This theory explains the lack of observed magnetic monopoles and the uniformity of the cosmic microwave background radiation. 