Lecture14: Cosmology (Part I)

hello everyone welcome to lecture 14 which is about cosmology in this lecture we're going to talk about what cosmology is and then we're going to go over the basic picture of cosmology that we've put together um in the early 21st century and then we're going to talk about some of the Mysteries that still remain in the field of cosmology let's first start talking about how we can Define cosmology probably the simplest way of putting it would be that cosmology is the study of the whole universe or the universe as a whole if we want to be a little bit more precise however what we could say is that cosmology is the study of the composition and evolution of the Universe on large scales by large scales I mean large distances and in particular I'm talking about distances that are roughly around a few hundred million light years in the slides here I specifically have 300 million light years but this is not necessarily a hard and fast number the point here is that the Universe on these large scales at these distances and larger has certain properties that it doesn't have on smaller scales we will get to this in just a little bit but essentially what we do in cosmology is try to understand what are the equations what are the principles that govern the composition and evolution of the Universe on these large scales lastly I want to talk about what we really do in cosmology well this could be answered in a number of ways but one way it can be answered is that we apply the concepts of gender relativity Einstein's theory of gravity and thermodynamics to the universe thermodynamics is the study of heat and energy therefore we study gravity we study heat study energy we study particle physics there's other things thrown in there as well and we combine all these things together to understand how the universe evolved and what it's composed of let's talk about the basic picture of the universe that cosmology gives us there's a Foundation of cosmology or foundational story if you like and this is called The Big Bang Theory and this is a model of how the universe has evolved over time uh and therefore it's a model that tells us what the universe was like in the past and the Big Bang Theory by my count makes three essential assumptions or not assumptions assertions these are the principles of The Big Bang Theory and each of these is buttressed by evidence and I'm going to go through what that evidence is and this is how we can say with confidence that these three things are correct the first thing that big bang uh The Big Bang Theory says is that as the universe has aged it has expanded and cooled and therefore if you go back in the history of the universe the universe was smaller and hotter the second thing it says is that Adams formed when the UN was cool enough for electrons to bind to protons and uh this occurred roughly around 380,000 years after the big bang and then in addition nuclei formed actually this precedes um the period I was just talking about but nuclei formed within minutes of the Big Bang therefore the Big Bang Theory explains the formation of nuclei within a few minutes and then after about 380,000 years finally we have the formation of atoms remember an atom is just a nucleus with electrons around it and the vast majority of atoms in the universe are hydrogen and helium the third thing that the Big Bang Theory says is that once atoms formed the radiation that um permeated the universe at that time uh no longer interact Ed with matter before this period 380,000 years the radiation that existed in the universe was constantly interacting with electrons it was constantly knocking out electrons from orbiting protons if you have an electron orbiting a proton that's a hydrogen atom before this time and the reason why this time is this time versus any other time is that before this time radiation had enough energy to be able to knock out uh the radiation that was perating the universe the background radiation had enough energy to knock out electrons as they were orbiting protons so therefore hydrogen atoms could not permanently form at this time the universe cooled enough so that this radiation no longer had that amount of energy had just uh less than the required energy and um and therefore this radiation no longer interacts with these electrons and hence it just bounced around the universe as it uh did before but this time it no longer interacted with electrons now that we've gone through the basic assertions that the Big Bang Theory makes I want to talk about some myths and then I'm going to go into the evidence for the Big Bang Theory notice that in these three pillars if you like or assertions I didn't say anything about the origin of the universe one of the myths is that the Big Bang Theory says that everything came from nothing and the uh reality of the situation is that we don't know where the universe came from this is a matter of debate The Big Bang Theory does not make any assertions about this there's a good reason for that which I'll get into in a bit but the Big Bang Theory really just helps us go back in the history of the universe to what we call Early times I won't Define here what Early Times mean maybe I'll get into that a little bit um but in any case it allows us to go back uh into the history of the universe once we go back far enough however our physics breaks down and therefore we cannot go back to time equals z or even um to say if there was something before time equals zero the second thing is that there was no explosion the Big Bang was not an explosion this really is incorrect for a couple of reasons the main reason is that an explosion implies that there was some matter that existed in a particular part of space and that matter then exploded it's uh it essentially degraded and the matter particles moved into different areas of space that's essentially what an explosion is the Big Bang was not uh an explosion in this sense at all what we mean when we say that the Universe um has been expanding over time since the Big Bang is that the Universe um has gone from a small hot State into a larger cooler state one of the consequences of this is that there's no center of the universe or slightly more accurately every point in the universe is the center of the universe imagine you have a room or imagine you're in the vacuum of space it doesn't really matter and you have this is your space this is everything you can see and then you have over here a little box that has some explosive in it explosive material and this object object then explodes by studying the motion of these particles as they leave this little region of space You Could reconstruct the explosion you can go back in the history of time and you could say what this region of space looked like in the past and then eventually you had good enough data you'll be able to say that these particles all came from this tiny region of space and that there was an explosion this is not at all really what the big bang was this is not our conception of the big bang when we say that the Universe has expanded what we mean and I'll go into this in a little bit more detail in a bit but what we mean is that every point in the universe has expanded about every other point so in a sense every point in the universe is the center of the universe for example suppose as I draw this here suppose that okay I'm drawing something up here but I'm going to just describe it in words here I don't have enough space to draw it suppose that you had a time machine and you could stay you with all your thoughts and everything but you could go back in the history of the universe and you can just look and see what was around you at any time in the universe's history you get in this time machine and it has Windows you can see out and you go back in the history of the universe you go back past the dinosaurs past the formation of the Earth in the solar system you go back all the way to when the universe was really really small let's say the size of a quarter so where would you go if you could go all the way back in times the universe was that small the answer is that everything around you would crunch down so that you and the entire universe would be that small but you don't go anywhere you stay in the same spot and every point in the universe just contracts uh down so that all distances are within the size of a quarter so my point is that there's no particular place in the universe where you could say the universe expanded about this place there was an explosion here and then that caused everything um that we see that explosion eventually created galaxies and gas and stars Etc and this um person I'm using hypothetically you in this scenario this could be anyone and you could be anywhere in the universe you could go to the other side of the observable universe and you can perform the same experiment and you'd see the same thing I'm belaboring the point a little bit but I'll get back to this uh concept that all points expanded about all other points a little bit later in the video the third thing I want to say is that the Big Bang Theory is actually pretty mundane it sounds like some Grand theory that explains everything or is very mystical actually it's not really we use Einstein's theory of gravity and thermodynamics and and some other relatively basic principles in order to explain what the universe was like when it was younger and as I mentioned earlier we can only go back so far because our physics begins to break down at a certain point um so the Big Bang Theory is not really grandiose despite its name it's actually rather basic although it's extremely successful and it's amazing that we can go back in the history of the universe and say with confidence what the universe was like as a result of what I was just talking about uh and the evidence that supports the Big Bang Theory it's not controversial within the scientific and especially astronomic astronomical Community excuse me it's not controversial at all and considered the standard model for understanding the universe let's finally get to the evidence for those three um principles or assertions or pillars whatever word you want to use for The Big Bang Theory I said a couple of things I just wanted to quickly go over them as I know there's a lot of text here I said a couple of things about what Big Bang Theory says regarding the universe one thing it says is that as Universe has aged it has expanded and cooled the second thing is that nuclei and atoms formed within a few minutes of the big bang and then after about 380,000 years and then the third thing I mentioned is that this rad radiation at this 380,000 year mark no longer interacted with matter and then just bounced around the universe and we should be able to observe it today I didn't mention that part but I'm going to let's go over the evidence for each of these pillars this is not necessarily in order um if the order doesn't matter but anyway I'm going to talk about the cosmic micro background radiation first this really pertains to the last thing that I mentioned the the last assertion really says that there should be a background radiation that is a relic from The Big Bang that was number three now I'm going to make the evidence for this number one um this is extremely important because this background radiation gives us a picture of what the universe was like when it was 380,000 years old I might go into somewhat more Det about this because this is really important um I'll just talk about the the evidence for now um and what this actually is and then maybe I'll go into that um as I mentioned this is a leftover radiation from 380,000 years after the big bang this was actually discovered accidentally in the 60s I always forget the date but this radiation looks like static if you no one has an old school TV anymore but if if you turn on the TV to um something that's not a Channel or a channel you don't have you just see static meaning random noises and U visualizations and that's essentially what the cosic microware background radiation is the reason it's microwave radiation is because as the universe has expanded and cooled so has the background radiation in the past this radiation was much hotter but today the universe is quite cool the background temperatures about 2.7 Kelvin that's something we observe and that's the temperature of this background radiation and hence its microwave and microwave radiation is not particularly energetic because this radiation formed on a cosmological scale we expect to see it from all directions it's not something that formed in a particular part of the universe so if you take a telescope that can measure uh microwave radiation and you point it in any particular direction you expect to see this radiation and in fact it should look the same and indeed it does I mentioned that this was discovered by accidents I should just go into the story a little bit um actually I think I have it later on in this lecture I apologize I don't want to get into the details now but in any case uh today we study this in detail and we get a ton of information from this background radiation by the way it's called the cmbr the cosic microwave background radiation or sometimes CMB I'm just going to refer to it as a cmbr instead of saying the whole name so that's one piece of evidence for the big bang by the way this radiation the cmbr was predicted years before I believe it was predicted in the late 40s if I have my dates right um it was predicted years before it was discovered so this is what we expect if the Big Bang Theory is right the second thing I want to mention to you regarding evidence for the Big Bang are the relative abundances of the Light Elements I mentioned to that we use thermodynamics if we go back to a few minutes after the big bang around that time we can use thermodynamics a study of heat and work and also we need to know something about nuclear physics and we can predict how many elements of each type were produced as the universe cooled by using thermodynamics and nuclear physics we can make these predictions and then we can go out not literally go out but we can take our telescopes and point them into different areas of the universe and we can collect evidence for What proportion of elements are in the form of helium um excuse me hydrogen versus helium and we can even predict how many helium 4 atoms there should be relative to helium 3 for example the difference being helium 4 has one more Neutron and these predictions are accurate U for example virtually nowhere in the universe do we see less than about 25% helium and I'm talking about large scales I mentioned several times that whenever you are talking about a large collection of gas whether it be a star a nebula a Galaxy whatever interstellar medium you should always think mostly helium I'm sorry I'm misspeaking today mostly hydrogen about 75% hydrogen or so with about 20 to 25% helium and we see this proportion repeat itself everywhere the sun distant Stars galaxies Etc and the reason why hydrogen and helium always come in these uh in this proportion is because this is the proportion in which they were produced in the early Universe the early Universe was uh very hot and we know from thermodynamics and nuclear physics it could have produced only Light Elements and in very specific proportions we do not um find from our laws of thermodynamics and nuclear physics that the early Universe could have produced heavier elements basically essentially any elements heavier than hydrogen or helium except in Trace Amounts and therefore virtually all of those elements were produced in stars or in Supernova and this is buttressed also by observation because we know that the vast majority of elements in the universe are hydrogen and helium with some Trace elements finally we get to Hubble's Law how do we know the universe is expanding how do we know the universe was smaller when it was younger uh the reason is hub's law hubbles law was or is I should say named after Edwin Hubble who discovered it in 1929 actually infamously his 1929 paper contained poor data but he was lucky because it turned out that his conclusion was correct even though his data was bad but since 1929 we have collected much better data and we know that this is indeed true and Hubble's Law States as Hubble stated in 1929 that virtually all galaxies are moving away from us and the farther a galaxy is from us the far uh the fastest excuse me it's moving away from us right so the farther a galaxy is the faster it's moving away from us closer galaxies therefore are still moving away with rare exceptions but they're moving away at slower speeds and this should be a lowercase I sorry I don't know why I have weird typos um okay so we call this by the way recessional velocity we say that galaxies are receding from us so moving away from us and the farther an object is by object we really mean Galaxy the faster it recedes this law was predicted by Hubble Based on data I mentioned his data was bad but we've observed uh this phenomenon with a huge amount of data now in the early 21st century and it really is true that farther objects recede faster I want to go through these in detail because there's a lot of um detail here that I didn't cover because I'm just giving a summary let's start with the cosmic micro background radiation number one on my list this is the cmbr this is a picture of the early Universe specifically when the universe was 380,000 years old now I'm going to refer to the age of the universe going all the way back to the big bang and I'm going to presume that there was a time equals zero let me actually just stop here here and give you a little bit of a disclaimer when we plug our uh data into our equations specifically the cosmological equations we get from general relativity Einstein's theory of gravity as well as our understanding of thermodynamics what we find is that the Universe it has expanded and cooled over its history I mentioned this to you so when it was younger it was hotter and smaller if you go back far enough our equations predict there was a t equals z when the universe was born and at that point the universe had no volume no area just a single point it was a singularity if you will um I just want to go into this detail because I mentioned this concept uh just in passing but I should mention it in a bit more detail ale um okay I maybe should have spent time here discussing this but um I just want to do this now um so I mentioned that the Big Bang Theory is rather mundane it's not grandiose or anything The Big Bang Theory does predict that there was a singularity at T equals z and all of the matter and energy of the universe was concentrated at that single point but similarly to our understanding of black holes although we we know quite a bit about black holes and general relativity predicts them we don't know what actually happens of the singularity and the same thing is true of the universe and so I'm going to refer to in passing this t equal 0 point The Singularity and I'm going to for example um say that this picture of the universe that we get from the cmbr which is the cmbr um is a picture of the universe when it was 380,000 years old what I mean by that is that this is 380,000 years after the tal 0 point at which our equations say that the Universe was created now as I'm going to discuss later in this lecture we don't know what happened at this point there may have been some bizarre mysterious things happening there may have been time or some events occurring before this point this is a bit of a mystery at some point before T equals z our physics break down they break down it's a matter of debate but they break down a fraction of a second after this T equals 0 point so I'm going to continue to refer to the Big Bang as this tal Z creation point with the understanding that we really don't know what was happening then okay sorry for that little caveat but I just wanted to be clear about that so in any case this is a picture of the universe when it was 380,000 years old with the caveat that I just mentioned it was taken by this satellite called W map Wilkinson microwave anisotropy probe this is just the name of a satellite and an experiment um and what does it really say what are these colors these colors are actually uh temperature variations what we know is that the temperature of the cmbr is very uniform it's nearly perfectly uniform but there are slight variations in this temperature I actually have the average temperature here it's about 2.73 Kelvin bit more precisely 2.7 548 and uh the variations positive and negative uh correspond to one part in about 100,000 and these variations are depicted by these various red green yellow blue colors that's what this color variation means it looks like the temperature variations are much greater than they really are and that's just to uh ensure that the picture has some decent resolution so you can see it but really the difference between the Deep Purple and the red is just one part in 100,000 this therefore means that the Universe on large scales which is what we're studying in cosmology is isotropic and homogeneous homogeneous means that the energy and matter and temperature are evenly distributed meaning that you can pick this part of the universe or this part or this part and you'll find variations but those variations are very small the universe is also isot Tropic this is a slightly different concept this means that if you were to exist let's say at this point and look out well this is misleading this is from our perspective uh aliens if they're our aliens would see the same Cosmic micro background if they live let's say in another part of our galaxy they would look out and they would see the same thing and uh we would be at the center of this picture but would be at the center of their picture and they would see basically the same thing so uh in order for my analogy to work here I have to put at the center but anyway suppose that you are somewhere in the universe a random point and you're looking out as you look out you will see the same thing in every direction and that is isotropy okay so this is a cmbr the cmbr is homogeneous and isotropic I'm going to go through these Concepts in more detail in a little bit later at the moment I'm just introducing them remember homogeneous means evenly distributed isotropic means it looks the same in all directions there's an enormous amount of information in the cmbr I'm just giving you an simple snapshot but we studied the cmbr in great detail and uh we can then compare our models of the early Universe to the cmbr and in doing so we can say something about what was happening just a fraction of a second after the big bang although as I mentioned earlier that's a speculative uh time and at a certain point as you go back in the history our physics breaks down entirely but nonetheless we can actually go back quite far okay I'm going to um maybe say more about the cnbr but I'll leave that for later this slide just summarizes some basic facts about the cmbr one that I already mentioned is that it varies by about one part in 100,000 and therefore it's highly homogenous and it's also isotropic because it looks the same in every direction it was predicted in the late 40s I was WR about my dates by these two physicists and it was discovered by accident by penus and Wilson I mentioned that it really just looks ecstatic and um it was discovered by these two physicists who were I don't remember exactly what they were doing but they weren't looking for the cmbr but they were getting static in their experiments and they thought it might be related to pigeon poop or some um some error in their experimental apparatus maybe caused by pigeon or maybe not and then eventually they realized that the static was indeed the cmbr and they won the Nobel Prize for uh getting static in their equipment that wasn't pigeon poop that's basically what they got it for so anyway let's go over what isotropic and homogeneous mean in a little bit more detail I'm going to start with homogeneous actually I know it's a second one here but this one I think is more intuitive you may be famili with the concept of homogenized milk this means that the cream part of the milk has been mixed in with everything else if you let milk sit you will see it separate this in the olden days is how people used to get their milk used to be delivered and the cream would be at the top I'm not old enough to remember those days I've just heard of these things in any case when you buy hom homogenized milk milk that's homogeneous it's all mixed in you don't find separate layers so that's what homogeneous means all mixed up so that every part of the milk is the same as every other part and then we have isotropic which is a different but related concept which means that something looks the same from all directions now you might wonder aren't these two things identical and the answer is no actually let's say that we lived in the center of this universe here this black dot that I'm drawing on the at the top right I'm making the black dot much larger than it was originally and we look out what we see is the same thing in all directions this universe consists of lines that flow from the center the center is wherever we are okay this is not much of a universe but my point is that if you lived in such a universe you would see the same thing in all directions um that's not completely true because you have to just assume that you're looking on large scales um but let's assume that we look um outward at let's say increments of 60° to make this a little bit more specific I don't know if I can do 60° 60 Dees would be something like this right so this is our picture we're looking out here uh through this field of view then we see pretty much the same thing regardless of where we look instead of looking 60° this way we could look 60° this way and we see the same thing however this universe is not homogeneous it is isotropic but it's not homogeneous because clearly these lines are not evenly distributed there's a much higher density of lines here than here so this is an example of something that is isotropic but not homogeneous if we want an example of something that's homogeneous we have this if I live in the center of this universe here this brick wall um and I look out I will see it's a matter of debate how uh similarly things will look if you look out things don't look quite the same actually in all directions but if I take uh large scales I can argue that things will look pretty much the same uh but certain this is a homogeneous Universe all right so that is homogeneity and isotropy these two um properties are these two concepts are properties of the Universe on large scales the universe is isotropic and homogeneous on large scales that is a cmbr I want to Rel atively quickly go through the relative abundances of the elements and then I'm going to do Hubble's Law and then we'll get into um some more details about how the universe has evolved remember what we're doing here is going through the evidence for the Big Bang Theory the first just to remind you since I know there's a lot of information is the cmbr and I've just gone through some of the basic properties of the cmbr we've learned that it's isotropic and homogeneous meaning the universe are large scales is homogeneous and isotropic now let's do number two which is the relative abundances of the Light Elements we predict what the relative abundances are in the uh Big Bang model we can use thermodynamics and nuclear physics to predict how much hydrogen 2 will be produced versus hydrogen 1 helium 3 versus hydrogen 1 Etc and um we end up with data or excuse me we end up with predictions and we can compare those predictions to data and the long and the short of it is that our predictions are very accurate and these predictions are made um on large scales meaning we look out into many parts of the universe and we figure out using spectroscopy what various gas clouds are made of stars Etc and then we can compute these abundances so once again just to remind you this is important the uh physics that we have thermodynamics and nuclear physics tells us that Light Elements were produced in the early Universe in very specific abundances which is supported by evidence these are the abundances we actually observe but the early Universe could not have produced heavy elements basically anything heavier than lithium and lithium 7 is produced only in Trace quantities anyway so things like oxygen um Iron nitrogen excuse me not nitrogen but the heavier elements that are in our bodies such as um Iron phosphorus sodium Etc these elements were produced in stars as we have learned in this course and elements heavier than iron were produced in Supernova now let's go on to Hubble's Law Hubble predicted in 1929 that I shouldn't say it's a prediction he claimed based on his data in 1929 that the recessional velocity of a galaxy is proportional to its distance from us and therefore the farther a galaxy is the faster it's receding from us and this constant of proportionality we refer to as the Hubble parameter that's H so hub's law says V equals HD V is the recessional velocity D is the distance this would be of a galaxy and H is the Hubble parameter this is approximate by the way this is not exact so it's approximate in sort of two senses U one is that the relationship is not perfectly linear but for reasonably close objects it is linear it's just V is proportional to D and then the other sense in which this is approximate is that if you look at real data you don't expect every Galaxy to be perfectly aligned on this line because this is an effect of the expansion of the universe but there are also local gravitational effects so for example close galaxies can actually be moving toward each other even though the universe is expanding and therefore galaxies should all be receding from each other galaxies exert gravitational forces on one another or really they curve space and that causes galaxies to move toward each other and an example of a galaxy moving toward us would be the androma Galaxy but that's a very rare case the vast majority of galaxies in the universe are moving away from us and they're moving away from us according to this uh formula basically I also want to say that H is known as the Hubble constant uh as well uh but this is a bit of a misnomer H is really the Hubble parameter when people say the Hubble constant what they mean is the Hubble parameter measured today and the Hubble constant really should be written as H with a little zero and this refers to the Hubble parameter measured today the Hubble parameter changes over time so in the past it was different than it is today this is um the following slide is Hubble's actual diagram from his paper he has two different lines here because he's dealing with different data sets and remember I mentioned his data wasn't very good anyway but hub's law says that there is one uh line here which is equal to H * D and that gives the velocity v = h time D and this so this is velocity here and then this is distance and this line um describes the expansion of the universe this data is not very good you can see there's galaxies sort of all over the place as I mentioned to you I don't have a picture of this but uh the data we've collected since then is much better and indeed shows that this um this equation we call hub's law is accurate the value of H today has been measured by a satellite called plon and um I just want to mention this to you since this is an important part of cosmology uh this by the way is infamously hard to measure but the current um well there's some debate about what the I apologize I'm having trouble drawing here okay anyway the uh currently accepted measurement is around 67 to uh 70 or 72 but there's actually some debate about what the uh value should be um I'm actually going to because this video is so long I'm actually going to do this video in two parts um I'm going to before I continue with uh slide 12 I'm actually going to um stop here uh this will be part one in part two I'm going to talk about some of the uh peculiarities of Edwin Hubble's data and then also some of the um some of the history of this and also the meaning behind hub's law and then I'm going to get into the nitty-gritty details of the expansion of the universe what do we mean when we say the universe is expanding I'm going to go into the different components of the universe matter radiation dark energy and um then I'm going to talk about the problems um that are still outstanding in cosmology okay so thank thank you for watching part one and I will talk to you in part two