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Cosmology | Lecture 6

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Webster let's calm disarmed observational facts or connections between observational facts and the equations it's impossible to really give any kind of justice to the observational facts without putting them in the context of the of fundamental cosmological equations so let's begin with them we've already begun with them but let's begin with them again and defying some observational quantities quantities which astronomers can Due observed but the basic equation was always at least for a homogeneous universe is the Freeman equation 8 . 8 square and that we can also do not remain weak in court the Hubble constant square of the Hubble somebody just recall Hubble French functions depends on time in the match finding Corporal are a function I suppose you could call it is valued at the present time I suppose you could call it the Hubble constant keeping in mind that Our constant born people call when they caught a Hubble constant there's is so many kilometers per 2nd per mega project would have reduced their quoting the value of the hobbled function today Orza scored a record the Hubble constant just forgive me I simply means a over 8 is the Hubble constant square as we that is equal to grow a prodigy over 20 times the energy density might a for the usual energy density my this attorney coming from curvature and curvature terms as Kelly in front of it is either plus or minus 1 or 0 never anything but plus or minus 1 0 0 positive for a spherical geometry negative for the hyperbolic geometry and 0 4 o'clock geometry provided by a square the role of Eddie is going to the mat threat for your right well I think we need more room for it right affect connection between any Internet Drake Is that the rhetoric yes squared minus D D squared class the radius firing squad 3 squared and I'm lose Ayala after river bracket DRS squared and that what goes In addition and angular peace and the angular piece is 1 of 3 possibilities depending on case the 1st will be flat space would a case of flats face that cake was wrong then this would be an aura Square D or may go to square the truce fear of scar where about Katie cost plus 1 where we put them remember signed sign of our squares so it was be sign of our square for negatively curved hyperbolic saga square square writer humid instead of writing 3 separate equation let's just call a city square Of wept see square has the following meaning is equal sign of when is equal to 0 plus 1 c is equal to 0 hyper box . cases you go from minus 1 thinks seed is equal . pay-as-you-go 0 that makes it was so our formula we just have to remember which
more users 3 different spatial geometries and an equation of motion for 80 reps are basic tariff fight now be edgy density could come from various sources the actual only sources that we really nor the current universe are of 3 kinds of 3 contributions the role and role peers as far as we could Delta have only 3 me important contributions 1st is radiation and radiation energy density is some constant representing the amount the number of photons per unit volume or the a number of our use of energy per unit bargain today are divided by acre before off as another contribution associated with ordinary particles nonrelativistic particles we usually call that matter and that's for bottom right you'll there's a possibility of vacuum energy what's actually put here at a party GE over free Americans continue to use a right hand saga wherever it at the end of vacuum energy would be times while the cosmological constant back those not by with increasing radius project but let's In the wrong a had in mind K over a square minor scaled a square a classless summer words West to include this over here as part of role and put here might escape Over a square sir I'm not sure why do that why he I took a week ago it now OK what's this I was a sequel to the sequel pay square it's Eagle beige not think about this equation today at the present time this struck set Of for quantities has up each square that took constraint that a certain set up for for corn produced has the end up each square now we can just how much the way how much can I trust and the present universe how much of a heading up the right hand side comes from radiation from which comes from matter how much comes from dark energy where and how much is left over in this curvature a reasonable question we scale factor today is some number We're talk about rule while how big it is barred some number each 1 of these Sharon's has some value and each has are you how we measure these votes in about how we measure from or how we might measure court on aid the Hubble constant Hubble measure the Hubble constant what it did was being measured the movie relation between velocities as determined from red shifts go back to register YRO he determined velocities as a function army having a distant your velocities from redshift Teddy Bear Stearns luminosity brightness by distant the blogs dimmer than the course so was basically redshift vs. luminosity poverty and cap and measured the Hubble constant think that's the factory measured missed that missed measured it by a factor of 10 that work was reported there are then strong we did was measured by the Arthur principle with better measurements and is 1 not cosmological measurements of labor cosmological army measurements taking place on a scale of tens of billions of light years these weapons measurements Of all local properties of 2 clusters of galaxies and so they did not penetrate back deep in the past but his purpose is to penetrating back in deep into the past the Hubble castles constant was Mookie at different times look Merrill while slightly quite now Burke Burke about thought yacht was is the city's all guy was all cars a story of a cosmic dissidents ladder Howell and it's a story of many different little pieces of overlapping go overlapping a distant the nearest stars the are you by parallax and then you find the stars are always behave in a particular kind of way course every variables behavior a certain very definite way and they have a very very definite relation between period their luminosity and all that you that you determine from stars which are close enough that you can get the distance from parallax
sovereign for sure there were a number purity and does that gave you a can or standard Campbell to work with a few variables you good then apply it to lure more distant the things very work your way up a ladder Supernaw are the best standard camels and would talk about that route talk about that cause loss measured by Richard velocity by Richard distance by sequence of overlapping standards the Burma work around are so far act it a yard yeah constants in the kind of radiation scales like vapor before matter scales or by loose like a vacuum energy doesn't buy mood and the curvature terms would you can't think others a kind of energy if you like in energy of curvature skills like a square OK Pablo measured age we do a better job of measuring age but basically you measure age by measuring the relationship between distance and velocity or red shift and luminosity but you want duet you don't need to go to a very huge huge distances to do boost our rule and therefore you're not looking back deep deep deep into a past of afterward to Brevard vary our problem with this now what about Our radiation well we can actually look at the amount of radiation the universe most of it is in the form of rugby cosmic microwave background which will come through but very feeble there isn't much energy the former before it took place a tiny fraction of the euro out of view the other forms of energy use and that would not just by measuring her video of the photons exist around us a black body photons ordinary photons and again there's nothing terribly cosmological about the measurement you don't have to go very deep into the distant past nor the you have to go over a away all you have to have a big enough volume average over but we pretty much know their radiation it is today in essential Barbara import OK outside well where we know about matters we look at the galaxies we see how much hydrogen is in then we see luminosity is coming out of the way make studies of star as we know a good deal about average stars and our from the average properties of star the gas and things which are technical but there are not not there conceptually terribly difficulty we measure all the matter but we concede luminous matter America be seen we ever walked past we have a pretty good idea as the years go on we measure better and better and better at a much lower than the average out the luminous matter is presumably all your form of Adams protons Our nuclei and electrons and we get an estimate of the number he added that number today he be density of energy in the universe today on the average is about 1 proton per cubic meter short very well are much higher than the radiation to be shot 1 proton per cubic meter exist for the moment let's forget about back energy boats who will come back to to it and little let's let's let's ignore it from moment young yes yes yes yes is about reaffirmed Monday was slightly star slightly hysterical a historical slightly historical young want I want To boost with a bit of a mystery in mind this is as it was when I was a young physicist books ROC radiation negligible seem that a substantial big deal broke on parole for cubic meter nobody believed there was a so if Rob worn by and had been measured who incidentally the relative radios of these the relative ratios of these the ratios depend on time because his skill differently but the ratios aII I'll called Omega service would not good values of views but the ratios ratios are Omega or are all made him on May land that Omega curvature for Mayor curvature may be negative and the rulers these must add up for the simple reason that definition is just the magnitude of and they provided by each square another words domain is Bobby fraction of each square contained in each 1 of these terms so as I serve as a young it was resource Everybody
thought may go are was equal to essentially 0 which Omega matter woes what you measure when you look out multiple white communion stars interstellar matter so for roughly 1 proton per cubic meter Omega land that nobody ever heard of the boy who existed our minds signed didn't exist and after so we then have a situation where we could
compute nor where omega k wars Ordonez going back this equation over here this time was negligible this was believed not to be negligible this was on an age should be measured 8 should be measured about a factor of roughly 20 or maybe 30 transistor where he S H & measure pretty well and it was too big the corresponding SCM over to another words the other words of this 1 he has had not been discovered this was negligible the Omega matter was something like 1 over 20 maybe world 30 a mature exactly how big roughly war over 30 this was small and the only conclusion was that Omega Katie was almost equal toward almost regal but 1 meant that K already square Amaya scale that square had to be close to each quarter what's right down Katie world we could say were a sign of cases immediately right beside of Katie has to be made was a 1st conclusion a sign of Katie is negative opened in follicularis support for K was negative and worn over a square equal the Hubble's measurement of each word now what dust why why white because this just appeared to be too small To a small the make up each where the only thing around the was big enough best and that turn called us all we thought a call how big 18 years In terms of now each has not meaning at least within the context neither Obama made universe let's go back to matter dominated universe which after all is what we have here right down the equation but remember aII the matter dominated humorous grows like keep two-thirds from most of the history of the universe back on this surely is not as important as the matter Sharon 1 over a square for small and AU with numerous was small was more at kind which this way that bigger but a lead times for most of the history of the universe are even tho the matter was pretty small was dealt with this Sharon for most of time competed favorably with Mr. this is regard this was a pretty good approximation Our the fails of late time pretty good early priorities and so let's calculate 80 over age 18 . 4 a or got a doctor's time derivative of key to two-thirds which two-thirds he wore minus one-third and then we divided by age so we divided by a Robert T minus 2 storage altogether a doubt over 80 it is just threw a threat over 3 feet so the whole constant we would affect we know how the Hubble constant varies with time in this model is a model of America dominated universe the Hubble constant we can write this down the Hubble constant away derived from current is is just a tool provided by treaty course are can't we can ask what is it that he is equation was being applied today so what is today the Hubble constant today is just equal or course H. today is just equal to a 3rd of the kind there was a time today meaning he age of the universe lets core capital E capital stands for the age of the universe other words how long it wars since the uterus was very small we don't know exactly how small but how how long the suits arbor scale factor was maybe you so many orders of magnitude more used to that's what it is at 1 that essentially worn over the age of the universe ought to be more exact a would-be two-thirds of the age of the universe 5 seconds to sure those voters flowed he was sealed lights no be units of the Hubble constant are 1 over par at the time successful which time at which time which units would you like to you that way U.S. would you like to you here and I want overturned but it is what it is fight whatever give site bordering on a stupefying the aging those of the units of nature of the virus from me the outlook who was it was on the relation between velocity and what is the connection between velocity this time so the Hall constant even know people with if you go a new-look learned Wikipedia or something the Hubble constant a book or something like 80 80 kilometers per 2nd per hour to pass for something something something I don't remember but the Mets of astronomers unit astronomers use EU paper because it's good for telescopes but from our theoretical point of view the Hubble constant is just worn over the age of the universe is at least for
dominated instantly if it was supposedly radiation dominated for radiation dominated religious matter only radiations will be key to the 1 half NH today would be 1 or 2 feet sold whatever kind of nice equation mistake you have for most equations of state the Hubble constant today is related to the universe age of the universe that's Guard OK soaring or something else OR from Hubble constant having measured it hobble no together said he was wrong where factor the Hubble constant too large remember and therefore the universe was too young by a factor of can be roughly a billion euros a year Samarkand billion euros but that's just from measuring Hubble constant saw Price sorrow but is seal on President her as for Linell yet from final he got it from the measurements for hours and I don't know that we have in the year a deep inside quite surmount looking at this equation here and saying This is negligible compared the latest while a square his age squared an age square is 1 over the age of the universe square it's telling us something about the size of the universe is telling us the size of the universe is basically the age of the universe is a speed of light in here talk AT is measured in Wayne he is measured in time and so is but this is telling you is that the size of the universe essentially lobby young the size of the universe is about he called the distance light will travel in the age of the universe but none was not true just little was expected to be true on the basis of Cosmo ology 40 years ago these equations dropping out various terms or talked to be negligible and as I said off 1 ingredient in this war several ingredients personal radiation negligible which is ruled on the matter being substantial bar still small only 1 proton cubic meter and only about 20 years side he and being as far as anybody who was 0 was thought to be 0 Basel 1 interact and that's why Foley's years people for what the universe of the radius of curvature of the universe was about equal what age something there we don't Norma figures drop OK the 1st column she had to do with dark matter source just talk about dark matter little bit work there were with I think probably most of you know the dark matter story but what our what they have made out of electrically charged particles radiates radiates want accelerated a radiates warned her are you call I would say it's called Lomas because radiates it's a kind of matter that we know about From mobs of from Virex telescopic observations it's what went to hear on the other hand is another kind of definition of matter which is how much a gravitate gravitates to watch the Mass Our matter which gravitates and of course 1st it was thought that the galaxies were made of luminous matter and that of a galaxy which is a luminous matter however it goes way back I know how far back what is went back the 1932 I did notice was a little bit later 1932 will be on the Dutch astronomer port or nurture produces Maine notice that there was something is wrong with the way galaxies will be here a year later Fritz wiki Corey did nor our the clusters of galaxies with misbehaving and misbehaving in meant that the gravitational behavior of them was inappropriate to Newton's laws also warned stars inappropriate to move laws and suggested that there simply was more a matter out there have been accounted for trauma work take it through that I think most of you know the story of dark matter and Yao said they if used guessed that have you 88 the allies could write yah yah how you separated showed diffuse almost everything radiates a little bit almost everything there the I don't want to see a massive black holes but it or you don't houses was young captains woman's appear now How are of course there's not matter of black holes but the point is doesn't matter we count was luminous matter not because of a small fracture the galaxy a center of black or not the fact that black or the center of the galaxy is roughly about anywhere between millions and billions sold the galaxy is tend not 100 billion Source pressures and Soros lead black coal plant the more a a major Dutch copies and besides certainly could not be the dark matter because of concentrate the center where the dark matter is of our rumor was or who
1st on the but it is not concentrate December guards just got through of the argument are the argument has those so-called replacing curves of galaxies the galaxy and you look at star as a different rate EIA and you look at their tangential velocity v let's begin by assuming something which would follow if all of the matter was woman the fact is that most of the luminous matter in the galaxy a center of the galaxy 5 by far the majority of the overwhelming majority of the material is at the center of the galaxy of the galactic center and so so far the gravitational purposes our things and they are a part of the galaxy are moving under the influence of a central force where the central force is just the massed near the center of the system we're on the lips of a logic of America but so are used those equations articles and may be gravitational acceleration dual messages sent there would be any kind GE provided by Ivory radius squared the star and that has the equally acceleration and the acceleration is velocity squared provided by radius acceleration was squared away aren't so this wouldn't say that the velocity pulls off like 1 or what are listed this somebody's Walker you know more is kept wall the kept was planetary Laura is usually expressed in terms of the period rather than the but this is essentially kept planetary law 1 of the walls which wanted a 2nd long where tell you how arm are of the velocity of planets varies as a function of the radius from the start more here and in particular its as the velocity falls off like moreover square remark velocity forward while score are as you weigh that's not foreseen by work of fabrics were seen by anybody since was seen user of is pretty much constant nothing angular velocity insolently it's not like this thing is rotating or a big giant can we're all are not the angular velocity on the linear velocity Bruyneel velocity appears to be constant I've how they account for about the way I know what a recount before is euros marketers more out source as saying all messes with the center-left said the messes distributor end let's say let's intervals are functions and of oil all are killed art is unknown the Marist contain will for Europe want to radius for all classes Europe where else are at distance are more under the influence not only constant at center both varying Mass would you varies like em of R and that case but but backed the equation energy our squared equals V squared off are what's multiplied by are now say the V His constant these constant forward who put here now and bar Baptist end but an hour all these constant doesn't change and therefore we find that and marvel are must overall like all are of multiplied by Oren think of V is a constant theme of ah increases as you move away from the center and so as you move our this is not a mass density this is the problem within the hour Our within a radius are apparently increases linearly with ah I tool our boundaries of the galaxy and even beyond that we see things would have been very very far images of galaxies we do see a straight star here and there and this yes this matter know much were dead that it's not just that magic just that's it is not the density of how last year when you're on the radio that he I know you're a delight being seems to a column if there if there is a few really I don't know where Obama but my guess is that by now people who simulate galaxy formation probably tell you that on natural thing our I definitely do not know a simple explanation for it are sold at the moment the looks like a piece of a lock year velocity curve was just flat I don't know a Europe was good substantial simple argument about 1 case so the URS all my colleagues anybody novels and people who work on galaxy formation but my guess is burned down or a combination of fixed on operational fact simulations of broke store that's a status of galaxies B the other thing is apparently because we know that from motion even from the motion of Gallagher's stars perpendicular to appoint
little looks as if this distribution of tariffs is spherical character rather than a conforming to these on spiral flattened shape of galaxies knocked over sure I do not understand why galaxies have spiral arms or why they look like quite disks are up more than 1 server put up in various places and you get some very complicated explanations it's not that apparently simple and certainly not the galaxy is going around like a pinwheel doing all our so about this dark matter just from the fact that it seems to be more strictly a distributed throughout the day and of our roses are the distances almost midway between neighboring galaxies warned can estimated by now are grab accurately how much dark matter very stock matters variety end users roughly a factor of some was between 5 him off Marseille factor farmers can I say that somebody knows whether it's a fiber carried by highways total was a look that up today and was mortified sort of birds whatever it is it's it's of order of magnitude tape times larger than the luminous may know why doesn't collapse and then bigger and bigger anxieties about bird the galaxy looks like this your pinwheel about that big the halo around there was quite a bit bigger why didn't turn why didn't they also fall together of the same way that the year woman well the rule in this fell together mean to say it a collapse was formed by losing energy and lost energy to radiation among other things it lost energy the collisions what kind of collisions collisions having to do with electromagnetic forces things and the process of colliding losing energy radiating a son of fell into the center to some extent sold what we need to expel them about the dark matter is that whatever it is it's much more weakly interacting in particular a not electrically charged now costs if a war electrically charged see it would radiate source not electrically charged for the fact that now electrically charged and that it is very likely rather weakly interacting maybe like neutrinos may be a little stronger America means that these particles that make up this halo here they circulate around me go back and for this way some of them are going this way some remembrance of elliptical orbits but they don't that with each other March and because they don't interact with each other in March although the period of 10 billion euros this pay matter has not collapsed and followed luminous luminous matter there is no question that the some degree they do follow each other there are no as far as I know no large lumps of dark matter that don't have some curve when this matter at center and I don't believe there are any galaxies are visible don't have Our luminous matter around but it doesn't follow they don't follow each other in detail that but the dark matter has a sheet which looks like a galaxy of under great big sphere are the halo uh this is was what I think a little here clusters yacht young better he was looking a promotion of galaxies and clusters or was the 1 who will be galaxies there are I understand he was 1st scale that got good that's right so there is evidence of this kind of thing on multiple scales it's not all or coming from galaxies commit galaxies his commentary interaction between galaxies are coming from home galactic clusters he's a star had a bad day had particles which everybody believe the mayor articles there doesn't get back lost saying we should think sorrow who is where are back saying forces so Levi said always yacht nor electrical force norms yacht be emission of gravitational radiation bodies stars and other things moving in galactic orbits and so forth is completely negligible on the year the energy balance sorrel radiation of gravitational waves not an efficient way to work for a lot of things to lose their energy phone surveys ratification head does and does it does are good it this is very likely that the dark matter this this was controversial for y don't think is controversial and more of that galaxies formed by 1st of dark matter collecting go Court in these great big pillows in the end be Ahmad Barry protons neutrons electrons assault force give falling each of dark matter halos at the bottom of big things with their 1st and then the reforms they form stars and probably I don't know how early the black hole formed the anybody but the black holes they have been consequences of simply while star forward together so it wasn't that the dark matter formed around the black calls the black holes are negligible amount of the year of the match sooner galaxies the galaxies formed as a consequence of the tables of but probably the way that work would be fire or not only somewhat yet which it would be somewhat young mean we think of the dances we think the density of dark matter near the center of the galaxy use significantly higher than your dark matter away from the galactic center and there for people who are looking for for example radiation coming from the annihilation of dark matter too dark matter particles colliding annihilating Foreman radiation where would you look you would look for center galaxy short sir yes more bad news Is there a way that we be know what level matter as it is gas if guests with probably just won't from particles we don't know we know we don't know but probably won't articles are was just me dust the means assemblages of large numbers of particles hold themselves together by wire by electrostatic forces by your or usual things hold things together ever those kind of forces existed between these those particles that these would be would not have survived because matter particles In the expectation expectations is that they are simply lonely particles a only or whatever moving was placed world is
part of a draft I think there not for a yes is probably song was probably somewhat abundance of their various letters from somewhat track young but the Is uses lost his bid bar got off so that as a healer goes 1 0 0 yard sale does that slated despite you go look up to spiral arms are galaxies tries to decide what should have thought some people think that a shock waves of star formation shock waves propagating round circles and we're not moving with the Galaxy there are moving with the dark matter harbors survivors of a picture was not a which I'm your wife From standards are introduced Rich as honorary white because they would be White likely would have to be pretty relativistic however much air relativistic particles orchestra 1 fact about these particles which is most important is that they clusters of vacated the cluster where gravitational Maksim cluster column things cluster less when their high when they have velocity if you have these particles had high-velocity they would tend to cluster last it's kind of obvious that if you have a gas of stuff as gravitational attraction hot it will tend to resist the clustering tendencies are attractive forces cold it will tend to warrant the cost of neutrinos being saw white with tend to be pretty relativistic there would be what called heart dark matter hot hot dark matter was over option sort of the dark matter for a basically because of this tendency a cluster of strong cluster is cold called me to say that the particles are moving wrote local reference frame with much worse the speed of light some neutrinos are not a good option for a no what His a year later he was there for that matter that wish there were these Song that that can't be starting over there that shocked by report yet but there is a lack of my hair down world feels like he did his assault on time up until the time this gets bigger than that OK right our after you have to correct answer Evita equation where of each is like 1 over tea that would get somewhat corrected but not a a lot because most of it was happening here earlier before a room before crossover points ahead to the roof for you may want to go work and out would work for use as it was about time that I had not a villages where our great we need to pay according to yesterday's Syria but today according to the theories OK so there was massive confusion was walk confusion about rest but I think if you were but things together without worrying about dark matter ambiguous had to say that repeat that of this term was big Bear wars of the signed K was negative end over AU was roughly the same as we age of the universe and people resisted it to some extent the mean reason I guess from I don't know what people were thinking each person was thinking something different but I think 1 of the other prejudices was that the universe was closed bounded so they would enter right he equations that were appropriate for K equals positive and that didn't and that conflicted with the observation so those a lot of confusion about later on 20 years ago or not sure exactly where it's also down that were there are the Katie was probably negative now what happened the leaderless command what the dark matter due to this equation well the left if we just ignore this the right side and the left side of the matter nominated turned over here and the Hubble constant differed by a factor of 25 or something like that so was pretty serious a big gap between these 2 at best the dark matter is 5 or 6 or 7 times a woman matter and it did not fixed is fixed it somewhat but didn't fix it narrowed the search of her I didn't make the matter terms equal the Hubble constant while it was still not only left room for K already squared with negative curvature required required this term to still be there so it didn't it didn't while arrested and fix things I'm not sure fix me our nothing particularly wrong with saying that each square largely came from here but the matter attorney was not sufficient to work toward gap store however protein asked for it or not With while also it yellow it depends are actors the if particles or white firmly arms troubled can't go occupy change be moving together slowly relative to each other if their bows on which they can be extremely light and a B phase called on both the compensation and the ball was condensation just has very very slow particles all the strained quantum state movies like a bozo Bose-Einstein condensation and that is 1 of the theories of dark matter called the axial theory that the axiom credibly light very very worried the exact numbers but extremely like much much light neutrinos and a former Bowser a conversation that's 1 theory of dark matter and that's a good period Our crazy theory but mostly people think about series in which the dark matter are particles that could be detected in big accelerators particles was masks are in the range of NASA's could be discovered that the DOH Miss happy course army is a wishful thinking while you're out of right receive your most don't have enough sorry reached the but not in others there is no theoretical maximum on West used to mean that the particles interact with roughly EUR standard model weak interaction cross section and the maxims probably up a few P E V if you were a baby most 10 times TV and our deal I think before the user enough ah energy tour of detected them apparently not
Europe is more the 2 years so a more information and it is possible for will be discovered that they may have a right properties the dark about the way it is it's not the reason yesterday it is not because he was known honor they have particles that can be seen Makeni measures we don't measure every measure revocation E I guess you're asking is it conceivable that these are particles which are so unusual that we have almost no interaction with ordinary material and therefore we don't see but beyond that track but it is possible that they just sold weakly interacting with ordinary matter that us that there's no chance of detecting if possible fastest 3rd so in this part of the game can later be with no woes had what yes they were very very light yardarm if their bows undertook took a vacant both economy conventions and they don't have to to be moving out of affirming under have harm but that OK the ACGIH on theory is not a theory in which the ax yards where every thermal equilibrium if they want some 0 equilibrium at 1 time then they would be moving fast today hard work this is this is not where was going with shots lecturer was acts would we know what we know with any confidence nothing about are the most likely thing is some form of elementary particle that hasn't been discovered yet Tarver good chance that there heavy enough to escape detection the LHC but light enough to be able to be detected in future experiments that's that's about all we say a moment and then there's the other alternative for the dark matter worst of modifying gravitational theory of attempt was lawyers who work for galaxies firm that doesn't seem to worker don't seem to be any nice modifications of standard gravity theory which explains Charles most or Singh particles but freedom cover theories as 8 cases to a total yes by was federal there's not so by that there's a negligible dark matter around jazz right back pressure young Keaton wearing your density of matter and solar system is her a lot higher revenues a you were high Barker matter in the solar system was not compete with the gravity of the song not by a long shot Russia doesn't proposed effect from soldiers OK hat 5 it's now it's natural and fast food maker how we catch up with fresh candidate theory is can hearing candidate areas matter dominated forget this may refer Gavilan there because some free there are we hadn't heard about here is negative end negative curved space How request editors recast any particular model a marvelous Bentley consists of 2 things it consists of a specification of Katie whether 0 boss 1 minus warm and some kind of equation of state for which you could substitute a history an 80 of tea and a F T and is a marvel that you could try that fast so what what billion nor or learned what kind of drummers measures and how they compare it With a particular armed with a particular marble while I watch the same day the pretty much the same thing hobbled except a sophisticated version of a bomb you can measure to things tho large extent you can measure the redshift of things which tells you something about the velocity and Ukiah and measure distance by our by luminosity how goes 2 things come together tell you anything about the American Katie and 80 of sorts talk about thoroughbred 1st let's ignore the fact that each of the the Hubble constant changes with time and West just suppose we didn't have to worry about the fact that the universe balls was just supposed from that it would Over was off an instant and that change what could you do to measured case where universes open or closed or what end the way to do that the measures the number of galaxies are there of a given brightness what does the brightness have to do with case sorts talk about that body if the number of galaxies as a function of distance really that's what you want 1 measure the number of galaxies for this to happen the think dissidents is related to redshift which of course it is then you could be talking about the number galaxies as a function of redshift but let's just talk about the number of galaxies as a function of distance with distance is measured in some way that woes that we need to come back to bite off therefore led a flat of William flat our clear and spaces homogeneous homogeneous that's pretty clear but relief a number of galaxies In a region DRR say with Michelle surrounding osce distance are are grows like or squared as does the value on radar Square D R it's also true that if we would've negative curves ladies it would go like hyperbolic sine square of R and that means something which grows exponentially with our E the tool bar Dr if we brought us here the crew living this of space was this will become sign of all are square br but let's forget about me evidence the seems negative curvature this is a case for negative curvature of the 1st thing you could say he is the number of galaxies as a function of dissidents would grow old much much more rapidly as a function of distance on what about as a function of luminosity work is a functional luminosity Houser luminosity particular another question you could ask is how was luminosity depend on this Waterhouse luminosity depend on distance and flat space on whatsoever because our core or
squared with sister it's just leave the same back here all white all but the center and passed out here than luminosity of light bulb the amount of radiation coming out would simply be spread all over the area of the sphere of urine area grows like our squared so the luminosity itself cause like our squared but opposing you will living in this negatively current where the area this year grows like Peter the 2 are then voluminosity who would be March a much smaller so what you would find would be a very rapid fall off of luminosity with this you if find many more galaxies out then a given distance but you would find the luminosity as a function of distance would for off much faster so particularly you could ask What about luminosity is a function red chips and you will find the characteristic behavior of the luminosity as a function of redshift which is stable luminosity really gets small fast because of the C. Itoh to are so that would be that's that's pretty much the way of determining whether Katie's plus 1 minus 1 or 0 0 that Our particular cases my this warned me the negative curvature 1 should find that beyond the number of galaxies at a given distance or a given redshift anomalously grows rapidly with richer as a red shift forget Our deeper and deeper into the red a number of galaxies should grow much faster than the would based test you could also think about calculating the number of galaxies but you see as a function of redshift from legality you see as a function of redshift forget the them this in the brightness from just galaxies DUC each redshift of something you could also cut reverse talk about where are you do that why not talk about a we are program redshift was registered press a flight is mediated by a source but Hauser wavelengths y Amber sleeping call at the wavelength of light 40 minute emitted just usual white ball but has a certain were detected the light may or may not have the same wavelength there could be various reasons for a shift of the wavelength Poplar shift as warned gravitational redshift girl from from gravity do little black holes of 1 and the expansion of the universe which happens to be a quote from Doppler shift laughter or its equivalent of publisher the expansion of the universe is the 1 that were arrested he here is what is going on but strong map bravura sisters time Karzai cost base and here today where a right of assent editors are equal 0 different are correspond to different vertical lines she uses Oracle's 1 Oracle's to Oracle's 3 so for we look back we look back along like rays so how light rays moved well and class-based Kowsky rhetoric remove on 45 deg wife but this is general relativity is a complicated matter will will discuss a little later how libraries mobile only more than will somehow you straight lines are curved trajectories somehow libraries will figure that out later we look back always regards your here with galaxy over here with regards to UMass you go here we see them at different times because we see them at different times we see their 1st of all With different scale factors the scale factor various vertical year after as Mayor City up here this today let's call at a today he really an issue point over was just call a the light emitted over here has the correct get year universe increases by a factor of of 1880 over 80 at emission time day-to-day canoes before was a number of AT&T emissions prime depends on emissions that's a factor by which the wavelength of 80 electromagnetic waves will stretch roar from here to here and that's a fact the redshift factor always defined redshift carefully with supply Richard referee is the the ratio of land when he had been provided by a Lamborghini myriad Anders that's not quite right minus 1 plus 1 person Armed Midas war my use water why is 1 they have for historical reasons call Z is RHF land that detected overland emitted is just the ratio of 8 today over a year so we look back on a library we see light emitted or here we see light over here we see Liberman over here and each mission has a different redshift 5 the redshift factor this was this minus 1 musical to zinc AEK very young this minus 1 musical because so if we know the scale factor at the time of emissions than we know what Zia's pockets about God arm but so far we don't know anything because we don't know have a white rebels until now have a right way way of life removed we don't know our compare these points so let's talk about how White Label work out things we need and then write down equations for you which are a which astronomer were actually work OK so what's Alexa has a light removed we go back to the Met over I raise on already light raised particular light rays are moving radially relative past few we are over here like races will be radially cars on all raise which means he scored his equal pay of peace where times beyond square right then foreign all ready for a White Label backward like that imaginary backward moving library that D. 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8 Eddie what what's varying that a car they varying bearing a state that I was raring as you look back along here it is AT at the initial point if she's so that's equal are differentiate 1 already so rats Martinez a if he squared different or already is 1 of squared times DEA right BART of everybody recognize that equations so we have to provide by that's my yes acre over a scored there'd be a for his Beery yet 8 is DEA by deep private DTD am varmint when the pure review cordial Robot became PGD fears ER rely quite that quite look like Dr the sword that now we have DR by see what's areas are by is more in this 1 already have tea also like that's why I had to to do this so I had to figure out what us from a lot of these so we are and they are by decay is my as 1 over a select a sort of a minus sign N gives us parity another 80 downstairs cancel was scary cancer of Vicente world well market but notes I users what saved what day-to-day Ave zip plus warrants Sarita they owe a Z course 1 OK so here I have the number of galaxies seen that Richard z contains a factor 1 was plus 1 rocket Elektra reps just the mold of Windows and then Nexium are provided by a doctor what we do with that see what we can do with it we can there's nothing we can do it and there is nothing we can do with it until we make a model until we make a marble cars but so let's make a marble Let's like a marble and what we get do we really wanna do this now doubt whether what story I make a model Our model is the matter dominated universe What's the matter not related numerous worth Katie equals minus warm from dominated universe for most of the evolution of again a looks like key the 1 truth his allure doorknocker go through the whole of go through the whole story we can calculate 8 . 80 . is equal to prove the Arabs are divided by war with one-third we calculated got what about aura to recalculate R yes we can calculate once we know aII of tea we can calculate all are won't do the calculations but we also know Forest see it's not written computers moreover once we know it aII we can calculate Zee the point is that Everything we got are can all be expressed in terms of z we know that a N A today we know the relationship between and with our relation between AT & T E another word we can write everything in terms of everything here is not only in terms of sea salt we get a thing year which depends on but it's not only because we stopped to a particular marble how I use the different equations state that we different answers of ah battle interest in quantity that exponentially increases were Vorel that's easy to detect that's really easy tactics Vargas explosive which is just increases were aura that means are increases with red chip that makes and are mostly large number of galaxies of large red shirts are case was negative and a dark could be computed directly from losing you know as a point there's enough flew over labor you could take a model which means that they Medicaid and converted into a statement of harmony galaxies UC per unit redshift together with the other piece of information which was the relationship between redshift Aaron and luminosity postal bits of information together can give you a complete history of the year the expansion of the universe that's enough to give you a completed a complete description of the expansion of the universe and tell you works Elora's I'm assuming something about you are but I didn't have to occur about this calculation flats closed universe the pieces of information are on a red shift or Richard luminosity as a function red Sheriff and the number of galaxies as a function of richer rose 2 things together are enough to determine 80 of tea and cake with plus 1 miles 1 0 0 so you that astronomers who have been doing it for 50 years or more and the final upshot is 1st of all he could assist with this matter dominated universe with Kate equals with being negative were consistent with the best fit the best fit from our Assembly mustard galaxies I need standard candles of crime and standard candles which are best that richest were interested in or supernova Supernaw offerings richer Avery controllable we can't control them but we can nature controls and the
result is not as formula all by Omega radiation again essentially equal to 0 on May got matter and this includes both dark manner and luminous matter dark matter luminous matter about . 3 made Orlando Bob . 7 end maybe Katie a abroad 0 this is observational facts know very little theories gone as well here is gone into it but no particular robbed biased news about 1 work to expect this is pretty much what they are biased raw data says and zeroing means it could be . 1 or it could be miners . 1 but only with could get back point or what could be beat point 4 walls . 0 1 plus or minus it could be that small could be that big and there is a bob . 7 Omega Man About . 3 that's the best fit for our various pieces of information here using models which depend on the equation straight Solheim just From count just Calpin galaxies redshift apparent arms and luminosity that's picture that emerges what it is that was not about today not talking about that at this model this theory failed failed failed this test it just could not reproduce video observed luminosity are numerosity 0 relations Indian music just did just failed but the way we on ladder is waited rabbit word I got is not new but it is not the you put in a number of reducing model consists of numbers Basra goes until model value of Omega value of Omega land value of matter or equivalently radiation is not portend Lambert end cape but procedures From board left a letter stating there is after dark hair you have the process it through bitch yup yes you think this'll you begin not orders to begin with a value of Omega Katie of value of Omega Lander of value will make him value make off yet values on number you stole a set of numbers that defines a marble value processor I wanted so the equations you run of the mill what you calculate is Elise E and B and you compare them will experiment if it fails you Mama away and put in some numbers and you keep trying numbers that 1 works that works with some uncertainties but they certainly is big this 1 is our small . 0 1 of their border also moral and I think this is . 2 8 the firm number 2 8 were ever with court . 3 so they don't talk about 1 per cent numbers on go about 1 per cent and a few very them very much much more than 1 per cent of these tests failed stop or a model then again a model consists of a specification of these values which needs the values all of the various components here today but you don't let them completely some measures some adult measure but you just feed them in grinder we also calculate any of tea from from Leon Friedman equation calculate if you want to have a you could feel they hear calculate PM by dizzy and luminosity function was contested it is a day were Missouri that was followed by yes well once you have a model year juggling various things but once you have a model with fits these 2 pieces of data OK then he'll have an 80 as a function of time and you could read offered what aid to areas and the Satsuma roughly speaking from the Hubble constant threat yet from marble crops so that is 1 of the output for me out is they earned Reuters says that pieces of Wash test for for fact if you were to gather this developed for a photo with that story it if say was is looking back that is if you only took your data from very very far perhaps the only turned the port here's this way is this 1 if you got a very small 80 which means long past this is simply a much bigger than the next they said that what lives EU look back the be all although over news Robert far less than last year start structure to bill you go back a billion years to billion years 3 billion years 4 billion euros the ruptured grow tried but that goes into these aggressions 80 of of tea as a function of C ways back up present you pirates go back to again To begin with a set of values Of the matter density very cosmological constant density are already used they going equation for what is now it is ahead of Villarreal is said ratio that also need to those we saw some are barriers we feed them into here we calculate the end by Desi that's an observable thing the number of guards is how the numbers galaxies varies with observer we calculate LOC that's also of observable thing if a model as a work with Norway
Streisand numbers well noise 1st where she those try and get try letter now trial on camera is yes you have to have a machine starts with a set of 4 numbers this 1 is the farmers for everybody knows this is arm for because you measure it directly small matter equation but details if the job is done with you but I will be not pass son luck this 1 this 1 here it is more or less measurable directly y you can measure H H is measurable Hannukah measures of the dark matter and luminous matter together and basically all may get him is the ratio of this factor or here as well as what you measure you measure the energy density and have a measure the Hubble constant and the ratio of them there's only so much that actually is measurable it's really this 1 it's really just 1 year which was the army so so what this 1 is pretty much directly measurable Omega was . 3 we were social yeah including the dark matter Omega views about . 3 these 2 are the ones which are marked ball what is known as recent theory is that this plus this course this past equal 1 this glasses assessed a quarter this was known former followers but knew 1 the better track really what you are doing you you really are over but I just don't want to say well as was . 3 this was not really known nobody's ever measured the curvature where are rare for this form must be points out of college or do you want to take this is given this is unknown and maybe cazique whatever it is the throughout the difference we remain because this was not this was unknown but won't put in as a trial and Omega cases was left over we but that Italy's equations we run at her we calculate rosy Indian by having done that we just look for the best of air probably query sold religious toward trial once more these 2 as well as 1 measurable is negligible . 3 these or unknown what's known for years that the sum of all of them should have up toward we take a test value from ago that tells us what land that is right the Friedman equations find our way of cheese having computer they have see we got this blackboard over here and compute the observable signature the number of galaxies per unit Z and these relationship between and after the relation between me and luminosity is a generalization of Hubble's original calculation luminosity years are a distant Z it is velocity no reason we have to do better is because will looking at a different car Saleh reinvest and the Additional ingredient is however these couriers knowing how how light move himself or that involves the model all the details of model who want to put the details of the novel way you look for you but the best is with these numbers here us to choose West retreated while only 1 event because they have some life what we fully you're ways so while guess what foreign aid for raises of death I result his oral they all that so what do want a young age wasn't your while wear while the war and then he bear guard you take best new Peggy you take your trial euros saw all the Friedmann equations with that tells you what I have to use for your model of feet into here this is not what you get you you get something different view that and calculate the number of galaxies per redshift or number of 0 Supernaw Correggio and will not go luminosity a function there that would say just think yet for our that was there only 1 way out why because this forces was assessed 1 right now but as I said that you just always it is really a lot no 1 is safe your force is businesses or opened 3 such of yes right right with disk rose above not was last to where they live 0 well aware formulated for former former 0 but Omega yacht from those a were there they were they were based where left for drive feel like a warm bath feels like the correct parts of the city right awesome the other others River white flood are reduced or rewards for you while you're the 1 million new users and correct there's this method relies on fears that did see the is isotropic space I know where I was yes to tropical 1st trial was a on a day earlier if the universe fall back or galaxies but and it is assumed that every time spaces homogeneous and isotropic if does assume rat on but you know that's so large
extent has did not completely but if you want to know whether it's isotropic at this time of year you just look at galaxies that you could see about Pyrenees such traffic in different directions redshift a priority register interest proper but not the it would be different so in euros days find the b the ratios have his country's foreign numbers CRR although a cover for class see em already to grassland miners Kaori squiggles age were best Troy all kinds of now with plug they now eclogue until a today delay but could now we just take a ratio provided crap just by billion years ago they differ Missouri in years ago during the question is is this you'll be rid of Rivers what they obviously we gotta be a wave of fear they are is conceded that long in the parish radiation was much more important than matter were much much more important than so long in the past a long long time ago 0 Omega radiation was large large means essentially equal to 1 long past Omega radiation was about all the wires and everything else was small there or feel are he wrote a letter yes I or maybe is May God secrets right now don't matter what worries me volume be E follies on May got her OK so what's the most a gets a large was going to be biggest lenders could biggest right so alone in the future of all go Amber will be 1 what may go on the way we won and everything else will be small off get curvature well less small Omega matter which will be less small in her memory radiation but long on the future it will be dominated by that long in the past it was dominated by radiation West what is the root of the matter obvious almost of these yes yes that's correct that's correct beauty the Omega start small because almost all Omega radiation but dip right get bigger stocks suffered dominated gives up near war with fully made-up Millwall close to 1 class before when the became important and then land becomes more important than this acts today so Omega matters . 3 from OMB . 7 water I'm glad the as well we don't know that we all know that what on handle it you right it's not the knowledge that that that's correct that's not going there when I said to us remote that I mean to say that we know of 0 to within the about a 1 per cent the next round of experiments might discover subzero might be what percentage postmark North Lerma launching much but our will change showing it will get smaller you will get smaller who have smaller because this rule will eventually defeat by any arbitrary amount so Yahveh soon will get smaller and eventually although B will be warned that far verdant our server for some series because in that of course dances and is is this a vision but still a rental no your own yacht nor the this has achieved a level of voter precision because more orgy were everything goes there are now the only good thing is it's a 1 percent what's not append the purpose of the 104 4 % 2 years 1 per cent Fred and everything efforts toward which I thought that this is formally values they gave us a huge blow angles got a correct that's correct order contract we study your next week a microwave background and the microwave background still lumping this a microwave background I was trying uation Rogers triangles again among my arm probably of Beaulieu uses supernova data which is I don't think that get ketchup % maybe it gets you somewhere between 10 % 1 % combine them supplemented with video recover cosmic microwave background form 1 ladies is a 1st for a yes or we are assured showed were gets a flatter kept as your 1st thing is why today's continues to grow 0 . will recall wire OK this this is tricky stuff but the way they think about as you start with the model which means a set of parameters here you feed them mental Freeman equations you got to decide what Friedman equations and you can read off From the Friedmann equations observable quantities Ghazi Indian by combined resist settling no reason why any particular set of numbers has to agree with data on series about a theory Our there be no particular reason why any set of numbers were removed data so it's not just testing a particular marvelous test particular model and the testing the theory for
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Titel Cosmology | Lecture 6
Serientitel Lecture Collection | Cosmology
Teil 6
Anzahl der Teile 9
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
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DOI 10.5446/15060
Herausgeber Stanford University
Erscheinungsjahr 2013
Sprache Englisch

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Fachgebiet Physik
Abstract (February 18, 2013) Leonard Susskind develops the energy density allocation equation, and describes the historical progress of the solution to this equation. He then describes the observations of luminosity and red-shift that have led to the correct solution for today's universe - which is dominated by dark energy.

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