Dark Energy, or Worse: Was Einstein Wrong?

[Music] think forward think research [Music] Channel the opinions expressed in the following program are strictly those of the speaker they do not necessarily reflect the views of the National Science [Music] Foundation from the National Science Foundation where discoveries begin this is Frontier discussions of today's most exciting research subjects by distinguished scientists and Engineers working at the frontiers of [Music] knowledge soon I will not be able to give this precise kind of talk because for the past 8 n 10 years uh we theoretical cosmologists such as myself have been coasting on the wonderful things that our observational and experimental colleagues have found you might know you probably have heard that we've learned a tremendous amount about what the universe is made of I'd like to say that the 1990s will go down in human history as the decade in which we figured out what the universe was made of and here's the answer in this little pie chart right here it's a very surprising answer only 5% of the universe the little yellow slice is ordinary matter by which we mean every particle that you've ever seen every particle that anyone has ever seen in any experiment ever done anywhere ever only 5% of the universe 25% of the universe is this stuff called dark matter matter that we've had hints about for years and years but now have really begun to quantitatively understand a little bit better and 70% or thereabouts is this even more mysterious Dark Energy so we've put all this together we have very good reasons to believe that I will summarize very briefly that this is the right picture but on the other hand it's not the picture you would expect if you've been given the job of finding out of coming up with your own universe as a homework problem you could have done better than this you would have made a much more simple and elegant Universe than this so the OB observers have given us this universe and we theorists have been going around giving talks about their work for the past several years and is now time for us to finally come up with some explanations for why the universe is like this rather than some other way so the real punchline of today's talk will be exploration along One Direction which is wondering whether or not this is perhaps not the right picture the only way it could not be the right picture is if something even more dramatic is going on so the title is dark energy or worse in particular I'll ask whether or not gravity could be failing us on very large scales so to get there let's start at the very beginning and whenever you hear cosmology talks you're faced with these really really bad analogies for what the universe is like you see balloons that are expanding or you see raisin bread that is expanding these are anti-h helpful analogies because they are objects that are contained within space within the universe the universe is all there is it's not expanding into anything 's no inside and outside it is the only thing that we have Universe wise so when I like to talk about the Universe I think it's actually best not to use analogies even though those are often very helpful pedagogically it's best to actually think about the universe think about what it would be like to stand outside on a clear night with perfect vision in all parts of the electromagnetic spectrum and you could also have a little spectrometer in your head so you can take red shifts you can do whatever you want the first thing you would notice besides stars and planets is the Milky Way a line of stars that stretches from one side of the Horizon to the other the Milky Way is a large collection of stars that we now know are mutually gravitationally attracting each other bound together rotating around each other in a collection of about 100 billion stars and 100 years ago as far as we knew that was the universe the Milky Way we didn't know there was 100 billion stars in it but we thought that that little island with empty space around it was a good description for everything it was Edwin Hubble who figured out that that's not true these little fuzzy patches that we saw in the universe were certainly not stars but there was a controversy as to what they were and Hubble showed that they were separate galaxies all by themselves so this is a picture taken by uh the Hubble Space Telescope which was named after Hubble this is a picture of an empty place in the sky you point the telescope at some place where you don't know about anything you let it sit there and collect photons and when you develop the film as it were you find a couple of stars there's a star there's a star but all the rest of these are galaxies there's um over 100 billion galaxies in the observable universe and they are spread out nearly uniformly throughout space so cosmology is the right science to specialize in for people with short attention spans because the universe is a very simple place it's homogeneous on large scales it's just about the same everywhere but it's not perfectly simple because it's changing as a function of time the universe is expanding Hubble again looking rather smug because he did after all figure out the two most important facts about the universe it is big and it is getting bigger he also played for the University of Chicago basketball team the last time they won the National Championship in 1909 so he has a string of impressive accomplishments to his resume so what it means when we say the universe is expanding we mean galaxies are moving away from each other so what Hubble did was to plot distance to the galaxies versus velocity this is a modern version of his plot you can see very clearly there's a perfectly straight line there so you invent Hubble's Law that the velocity is linearly proportional to the distance Hubble's own data were not nearly this clear in fact if you looked at Hubble's data it kind of looks like a scatter plant but Hubble drew a straight line through it because he was a genius and now we know that he's right so why does this mean the universe was expanding well if you're on this galaxy Which is far away from us you would observe us moving fast away from you in that direction and if you were looking in the other direction you would see that galaxy moving away from you so from our point of view every galxy is moving away from us but from every other Galaxy's point of view every Galaxy is moving away from them the galaxies are roughly created equal on very large scales there's no central point away from which things are moving so that's it that is the universe as far as you can tell just by looking at it in the night sky a smooth collection of galaxies expanding as a function of time if you played the movie backwards if galaxies are getting farther apart with a function of time now in the past they were closer together and you trace it back 14 billion years ago they were all on top of each other a moment we call the big bang so one of the thing cosmologists would like to understand is how did the universe expand as a function of time we don't know how big the universe is it could be infinitely big or it could be finite but we know the relative size of the universe at different moments in time so we call a the scale factor a number that is absolutely arbitrary but its time dependence tells us by how much the universe has expanded if a increases by a factor of two then all the galaxies are twice as far apart as they used to be so this is the kind of thing that is a good thesis assignment for a cosmology graduate student figure out how the universe has expanded as a function of time what is the scale factor a as a function of T so you can observe it a little bit but you would also like to compare to some Theory so the theory We compare to is of course general relativity given to us by Einstein you're used to seeing pictures of Einstein in the 1950s when he was a little bit older the hair hair had gone a little bit astray but back when he was inventing relativity he was a Sharp Dressed young man and someone was combing his hair this is from 1912 in between special relativity and general relativity and Einstein in 1912 was trying to think how do I reconcile Newtonian gravity with my new ideas about relativity the answer ultimately hit him to think of gravity not as a force propagating through the universe but to think of gravity as a property of SpaceTime itself in particular to think of gravity as the curvature of SpaceTime the geometry of SpaceTime the reason why that was important is because if it's a feature of SpaceTime itself it interacts with everything universally everything the same way if you're in an electric field positively charged particles and negatively charged particles move in different directions in the presence of an electric field but in a gravitational field everything interacts in exactly the same way that's why you can think of gravity as a feature of SpaceTime not as a force moving through it so here's the sun creating a curvature of the SpaceTime around it and here's the Earth doing its best to move in a straight line but there are no straight lines in this curve geometry so the Earth does a lazy ellipse once a year around the Sun and we call that gravity the nice thing about the universality of gravity is it gives us a way to inventory the universe you can find with quite good confidence everything that there is in the universe whether or not you can see it if you map out the gravitational field everywhere in the universe everything responds the same way to gravity and everything creates a gravitational field in the same way so if you map out where the gravity is you found all the stuff in the universe for example you can do gravitational lensing since gravity affects everything it affects the path of photons moving through gravitational fields so if you have a quazar in the background and a galaxy in the foreground the light from that quazar will be deflected passing by the Galaxy and the amount of deflection You observe tells tell you how strong the gravitational field is that in turn tells you how much stuff there is in that Galaxy so you can weigh that Galaxy just by looking the amount of deflection from the quazar behind it so I can't go into details because we want to get to other stuff but this kind of technique has been applied all the time and you get a consistent answer what you get is for example this is a cluster of galaxies this is a computer Reconstruction from data this is not a model these orange dots are where the galaxies are the blue is where matter is that is not accounted for by the ordinary matter that we know and love we have very good limits from big bang nucleosynthesis as well as direct counting on the total amount of ordinary matter in the universe it is not nearly enough to account for the gravitational fields in galaxies and clusters of galaxies in order to make sense of this we need to invent Dark Matter some kind of matter that is not ordinary that is not found in the standard model there's about five times as much dark matter in in the universe as there is ordinary matter so I skipped ahead so that's the answer we need more Dark Matter than ordinary matter but it's not the whole answer we've looked at individual galaxies and clusters how do we know there's not even more stuff that is in between the galaxies and clusters that we wouldn't have seen how do we know that we've gotten everything well we can do the same trick but we can do it to the whole universe we can weigh everything there is in the universe one way of doing that is to see how the expansion rate of the universe changes with time you have an expectation that as the universe expands the stuff inside pulls on other stuff inside and the expansion of the universe slows down gradually the universe is by the fact that the the mass within it pulls on the other masses so if you measure the rate at which the universe is decelerating as a function of time you're measuring the total amount of stuff how do you do that well nature was kind enough to give us a standardizable candle in the form of a type 1 a supernova a type 1 a supernova is a white dwarf star a white dwarf is an ordinary star that has exhausted all of its nuclear fuel it's very compact held together by the electrons just being pushed right together according to their degeneracy pressure so it can't collapse anymore it's not burning any nuclear fuel but it has a friend at this particular white dwarf and this friend is dribbling matter onto it so the gravitational field of the white dwarf is growing and growing and growing and ultimately the electrons will lose the white dwarf will collapse the layers will explode off and you see a type 1A Supernova here's an example the Supernova is almost as bright as the entire galaxy in which it is contained the good news is that the Shandra sear limit the place where these white dwars collaps and explode is basically the same for every white dwarf everywhere in the universe and the tiny Corrections can be accounted for and therefore the brightness of these events is basically the same so when you see them in the Sky by looking at how bright they appear to you you can figure out how far away the Supernova must have been so if you know how far away the Supernova were as a function of their red shift which is telling you by how much the universe has expanded you can figure out the entire expansion history of the universe and you get a surprise the surprise is the universe is not slowing down like you expected the universe is speeding up in other words if you looked at a single Galaxy and looked at it for 10 billion years it would have a certain velocity now a certain velocity 10 billion years from now that will bear larger that is the implication of this the Supernova that we observe are dimmer than they should be they're further away the universe must be accelerating this bottom curve here is what we expected the Supernova to tell us the top one here is where they actually are that's an accelerating universe so the question is how do you make sense of that idea we had a very intuitive simple picture that the matter in the universe would slow down the expansion the universe is actually speeding up its expansion well the way to explain it is something we call dark energy is the simplest possible explanation and what do we know about Dark Energy it's not that we know nothing we do know certain things Dark Energy must have certain properties to explain the data that we have for one thing it has to be smoothly distributed it can't be collecting into galaxies and clusters or we would have detected it through gravitational lensing but it wasn't there it has to have constant density or nearly constant density and that's what makes the universe accelerate ordinary matter and radiation dilutes away as the universe expands but Einstein's equation says that the SpaceTime curvature which is it gets a contribution from the expansion rate is sourced by energy and momentum so as the universe expands matter dilutes away and the universe slows down Dark Energy stays constant in density 10 Theus 8gs per cubic cm even as the universe expands therefore it gives a constant Perpetual impulse to the expansion of the universe and that manifests itself as acceleration finally it's invisible to ordinary matter we don't see it it is dark this is a picture that I took in my laboratory of a little cubic centimeter of dark energy but it is a false color picture really the dark energy is completely invisible it's just the answer to the question if you took one cubic centimeter and removed from that cubic centimeter everything removed all the particles all the dark matter all the radiation all the ordinary matter so that it was empty and you asked yourself what is the energy contained in that empty Cub ctim of space the answer has no reason to be zero in general relativity it's a constant of nature it is the energy density of empty space sometimes called the vacuum energy the vacuum energy would be absolutely constant and is the leading candidate for what the dark energy could be it's not the only candidate but we would like to check to see if this picture makes sense so the idea of empty space having energy is sort of a dramatic one we don't know whether it's right or wrong so we want to make sure that we're on the right track we want to check it we want to make extra predictions and check those predictions one prediction is that the Universe has a spatial geometry that is controlled by the sum of ordinary matter dark matter and dark energy these numbers happen to add up to one in units of what the energy would need to be to make the universe spatially flat the microwave background provides us a way to measure the overall geometry of space and it's consistent with precisely that geometry the Universe on very large scales is not positively curved like a sphere or negatively curved like a saddle it's flat which is exactly what the dark energy says it should probably be then you have the evolution of large scale structure as Universe expands and cools tiny fluctuations in density from place to place grow and coagulate into Stars galaxies and clusters but there is a compensating effect by the dark energy accelerating and pulling them apart so you make a very specific prediction for how structure should grow in the universe given a certain amount of dark energy and that prediction matches what the data say so this is a very brief overview of the whole picture hopefully you've heard of the general idea but I'm not going to go into too many details you can ask questions but we really do believe from a data point of view that there's no way to wriggle out of this picture if you believe in ordinary general relativity so here's the picture that makes sense 70% of the universe Dark Energy something is nearly constant in density smoothly distributed through space not a particle either some field or some property of space itself 25% Dark Matter some new particle some massive slowly moving particle that has not yet been detected in any experiment that we've done here on Earth and 5% of the universe is ordinary matter the entire periodic table as well as all the other particles in the standard model of particle physics this picture fits all of the data but it has issues let me tell you one of the problems that this kind of Universe raises you open the idea that dark energy exists then you open Pandora's box if you thought the dark energy were zero you could live with that even if you didn't quite understand it but once you say maybe there is some energy in empty space someone is going to sit down and estimate how much energy there should be in empty space in Quantum field Theory the vacuum empty space is not a boring place just like a single harmonic oscillator cannot be isolated into zero moment and zero position there will always be Jiggles because of the Heisenberg uncertainty principle in Quantum field Theory empty space cannot be isolated to Zero Energy Zero fluctuations there will be virtual particles for for example positrons and electrons popping in and out of existence all the time we know that these virtual particles are there that is not a controversial statement we have felt their effects they lead to the lamb shift in atomic physics they lead to all sorts of the radiative Corrections that are so important to high energy particle physics therefore these virtual particles are there they interact for example with electromagnetism but we've already said that everything interacts with gravity so these virtual particles should have a gravitational effect what is it is to contribute to the vacuum energy to contribute to the energy density of empty space so you can add up the gravitational effects of all these virtual particles and what do you get you get Infinity but that doesn't bother you you say well I'm a highly trained Quantum field theorist I've seen Infinity before I know what to do I need to regularize things and cut things off etc etc so we cut things off by saying we'll exclude contributions from virtual particles whose energy is larger than the plank scale the plank scale is this very high energy scale at which quantum gravity is supposed to become important we have no right to to think that we understand what's going on so let's not include the contributions from virtual particles with more energy than the plank scale then you get a finite answer for the vacuum energy an answer which is bigger than what you observe by a factor of 10 to the 120 famously the largest discrepancy between Theory and observation in any area of physics although that statement always tempts me to write a paper that has an even worse theoretical prediction than the dark energy I'm sure I could get something that was even more off than this not only is this prediction wrong it never had a chance of being right if you had that much dark energy in the univers a positive amount of dark energy it would accelerate things so much you couldn't make an atom much less a life form or a Galaxy if there was a negative amount of dark energy with that amplitude the universe would recollapse so fast a tiny fraction of a second that nothing would have chance to happen in the universe and therefore there's a school of thought that says this is just a selection effect that if this were not true if the natural value of the Dark Energy were right we wouldn't be here to notice it so as long as there's some place in the universe either some place in space some place in the wave function of the universe some place in the extra Dimensions where the vacuum energy is small that is where we will find ourselves that is certainly possible that's worth another whole talk and you can argue about whether or not that's religion or science and have a great time we're not going to have that argument today we're going to stick to the science end of things and this is where we are we have a picture that fits the data that's a good thing to have it involves general relativity Einstein theory is our model of gravity it involves the standard model of particle physics to explain the visible parts of the universe and it involves dark matter and dark energy as the invisible parts of the universe which can be very simply described and are enough to fit multiple pieces of evidence that something like that must be going on it's good to have models that fit the data but there are problems in our deep understanding of this model and this is where it's a theorist's job to do a better picture to bring a better picture to life the puzzles are how do you reconcile general relativity and the standard model general relativity is classical the standard model is quantum mechanical how do you make them talk about the same kind of thing what is the dark matter and what is the dark energy are perfectly good questions and finally for the dark energy why is there so little if there can be any at all so the fact that this picture fits the data but doesn't quite Mak sense to us makes us nervous the dark energy itself the acceleration of the universe was surprise it was not expected so now we're a little bit guny we're a little bit open-minded about missing something big is it possible that this picture is wrong even though it fits all the data we take those possibilities very seriously so let me just mention briefly one very interesting way in which the picture could be different and then I will go on to gravity which is the main topic the main the first way that I want to mention the picture could be different is if the Dark Sector of the universe the 95% that is both dark matter and dark energy is less uninteresting than we think if that makes sense you could say is more interesting than we think this is the picture we have right now that fits the data we have ordinary matter that interacts with itself via the standard model of particle physics we have dark energy and we have dark matter and they only interact with each other or with us through gravity not through any other direct mediation however this is 95% of the universe and it's 95% that we haven't probed in any great detail so again we should be open-minded about what might be there it is very possible that there are all sorts of interactions going on the dark energy might not be strictly constant might evolve there might be perturbations in it the Dark Matter might not be that boring it could scatter off itself it could annihilate the Dark Matter could interact with ordinary matter we certainly hope that this is true we're hoping to detect the Dark Matter directly someday and if we're very lucky the dark energy could interact with ordinary matter or with dark matter all of these are possibilities we are just at the very beginning of our exploration of this sector it may be boring or it may have a fantastically Rich phenomenology we don't know until we look I also want you to notice that all the arrows are correctly colorcoded here so that the yellow box and the blue box are connected by the Green Arrow I did a lot of work and no one notices this until I point it out explicitly so I want you to admire that just for a second so that is one Avenue that we are pursuing maybe the Dark Sector is there just like we think it is but maybe not it's not quite as quiet and uninteresting as we have right now maybe there's more stuff going on that's something to take very seriously the other thing to take very seriously is the idea that the Dark Sector is not there we only ever infer the existence of dark matter and dark energy through gravity we have been given a theory of gravity by Einstein general relativity which has been tested very precisely in the solar system but now we're applying it to regimes that are orders of magnitude away from that how do we know that our theory of gravity works on those scales that our inference that we need dark matter and dark energy is correct well we don't this is something that is not it's not a kind of situation where professional cosmologists are trying to protect the establishment and are trying to you know save Einstein's Honor by uh saying that his theory must be right even though the data contradict it as you might get the impression if you read certain websites all of us would love to be the first one to come up with a better theory of gravity than Einstein had it turns out to be difficult to come up with such a theory so the lesson of the rest of the talk will be that it is certainly possible to imagine modifying gravity to get rid of dark matter and dark energy but when you move the conversation about how that might happen from coffee table chitchat at conferences well maybe gravity's modified to writing down a theory to writing down an action that has consequences you re you realize that the experimental constraints we already have are extremely constraining and is hard to do everything all at once not that it's impossible we're still looking for it but that it is hard so where would you start if you wanted to invent a theory of gravity that was not general relativity well you could think like a particle physicist or like a field theorist general relativity is a field Theory just like electromagnetism is or qcd or the standard model how do you change field theories well you add new degrees of freedom or you subtract new degrees of freedom degrees of freedom are just ways that the fundamental fields in nature can vibrate for Gravity the fundamental field that we know about is the space-time metric the tensor field that tells us what the curvature is what the geometry of space is but you could imagine adding new degrees of freedom to the gravity just like we add new degrees of freedom to particle physics all the time once you add them you need to tell us two things about those degrees of freedom how do they propagate through space are they long range fields which would correspond to massless particles are they short range fields that correspond to heavy particles and then what do they interact with how do they couple to other pieces of matter these are the ingredients you need to give me if you want to say I have a new theory of gravity for you you say here are the degrees of freedom here's how they propagate through empty space here are their interactions for example you have general relativity G relativity has one degree of Freedom called the graviton it's a massless spinu particle you may have heard that of course we've never detected individual gravitons and we are unlikely to ever detect individual gravitons but we've detected very large scale coherent waves of gravitons they are what make the binary Pulsar spin down via gravitational radiation no one really believes that there are no such thing as gravitons it's just they're so weakly coupled that you can only detect them when there's a gillion of them piled on top of each other to give you a classical wave and even then it is hard as people at NSF will tell you and they're coupled to energy this is Einstein's other Insight every form of energy couples to gravity and therefore gives rise to gravitational field if you're familiar with gravitational wave astrophysics you know that what happens to detect a gravitational wave is you put a ring of particles in empty space this is the theorist way of detecting a gravitational wave not the real way of doing it you have a ring of particles in the vacuum with nothing around a gravitational wave goes by and it deforms the shape of the Ring of particles and there's basically two polarizations the deformation can put it into a vertical ellipse and then a horizontal ellipse and back and forth in a plus sign or it can deform it sideways into an X these are simply the two polarization states of this massless spin two field just like an electric field bouncing up and down or an electric field bouncing horizontally are the two polarization states of the massless photon of electromagnetism however if you think about what could possibly happen to a ring of particles you might say why don't we have a kind of wave that makes the Ring of particles expand in size and then shrink this is not what an ordinary gravitational wave according to general relativity does it keeps the area inside constant as those vibrations happen what about a breathing mode what about a mode that makes it expand or contract that would be a new degree of Freedom if such a kind of gravitational wave existed it would correspond to a scalar spin zero graviton you may have heard of scalar tensor theories of gravity those are theories of gravity that have as particles not just the massless Spin 2 graviton but also a spin zero extra degree of Freedom you can imagine such theories they've been imagined for years and years but they're very tight constraints on them you go from this sort of highbrow theorizing as to what could happen to actually testing it if there was a new spinless graviton in addition to the Spin 2 graviton we know and love it would slightly deform form the curvature of space time in the solar system in a detectable way so this is a picture of the Cassini spacecraft we told NASA that the purpose of Cassini was to take pictures of Saturn but the real purpose was to test general relativity so Cassini send signals to the Earth by the gravitational field of the Sun and there is a time delay when that happens which is extremely sensitive to the exact space-time geometry and the times that we observe that time delay allow us to constrain deviations from gr from general relativity one way to measure those constraints is to introduce the bronze sticky parameter this is a parameter Omega which goes to general relativity when Omega goes to Infinity so you get closer and closer to gr as Omega gets bigger and bigger the limit from Cassini is that Omega is greater than 40,000 by the standards of this game 40,000 is close to Infinity it's much much bigger than one if you had a simple spinzo graviton you would predict that Omega would be close to one it is not anything that you're to rule out absolutely because the coupling could get smaller and smaller and smaller this is telling you the coupling of that spin zero graviton if it exists is really really small it leads to a force much weaker than conventional gravity so that's the kind of constraint that you have to face up to when you're going to modify gravity we have tested gravity here in the solar system and it provides constraints more or less on all scales let me give you an example of an attempt to modify gravity in cosmology this is M modified Newtonian Dynamics invented by mgrm in 1984 before I even mention modified gravity let me mention an interesting empirical fact that mgram noticed he looked at the spiral galaxy rotation curves so this is a Galaxy it's some Stars orbiting around each other but there is also Dark Matter there there's also little wisps of visible matter that even though you don't see them visibly here you can detect how fast they're moving this rotation curve tells you the circular velocity of matter around this galaxy as a function of how far away it is what you would expect is that once you got outside the visible Galaxy the speed around which things orbit would go down Pluto moves much more slowly around the Sun than the Earth does because gravity is much weaker out there so You' expect the gravity would be weak out here and the velocity would be less but it is not in Galaxy after Galaxy after Galaxy ver ruin showed in the 1970s that the rotation curve is flat this was the first really strong quanti of evidence that we do need dark matter that the matter that you see in the galaxies is not enough so what mgram noticed in 1984 is that if you look at rotation curves of different galaxies there is a place in every Galaxy where the ordinary matter is not enough and Beyond which you need Dark Matter to explain what you see the radius at which that happens is different for every Galaxy but if you figured out at that radius what is the acceleration due to gravity Allah Isaac Newton 1 / R 2 milligram noticed that the acceleration due to gravity at which Dark Matter becomes necessary to explain the data is the same for every Galaxy the big galaxies the small galaxies spiral galaxies elliptical galaxies whatever you want there's a uniform feature among many many different galaxies that when the acceleration is less than that number you need to invent dark matter and he said to himself so that part is just true we need to explain that one way or the other mgr's supposed explanation was to say well maybe gravity isn't right maybe gravity doesn't go like 1 R all the time when the acceleration is larger than aot it goes like 1/ R 2 but further away the acceleration due to gravity goes like 1 / r that would be a stronger gravitational field of large distances and would give you a flat rotation curve it's an idea that fits the data where by the data we mean rotation curves of galaxies but we have more data in the universe we have the expansion of the universe we have gravitational lensing etc etc this Theory this is just not even a theory this is just an equation it's equation that applies to certain certain very specific circumstances does not tell you how the universe should expand what you want to do is to take this Theory and make it relativistic make it a full-blown model that you can apply to anything in the universe that was finally done 20 years after milgram's original Theory by Jacob beckenstein in 2004 beckenstein introduced a theory that he called Tevis and there's a bunch of equations on this slide not because I want you to understand all the equations but because I want you to understand why it took 20 years for beckenstein to come up with the theory Einstein's equation is one line with just a few symbols beckenstein's new theory has all of these equations stuck into it in a very very precise and delicate way in other words he needed to invent a whole bunch of new degrees of freedom the metric a vector a scalar field fields and L gr multipliers and have them interact in very very specific ways to invent a relativistic theory that reproduced mgm's idea sadly he did it finally in 2004 at a time when the data were becoming good enough to decrease anyone's interest in mgr's theory so you've probably seen this cluster before it was in the news the bullet cluster this is again a picture from the Hubble Space Telescope if you're a a practiced observational cosmologist you look at this picture and you say aha two clusters of galaxies there's a cluster of Galaxy right there a little overdense region there's another cluster of Galaxy right over there you could take the red shifts of these galaxies to show they really are physically associated with each other but there's an interesting feature of clusters of galaxies forgetting about dark matter for the moment think about the ordinary matter the hydrogen and helium and so forth most of the ordinary matter in a cluster of galaxies is not in the galaxies it's in between the galaxies and we know that because it in a cluster of galaxies the gravitational field is so strong that the that the ordinary matter Falls in and heats up to high temperatures gives off x-rays that we can observe so with the Shandra x-ray satellite we can look for where the gas is in these clusters of galaxies and that is where most of the ordinary matter lives but the funny thing happens for the bullet cluster is that the X-ray gas is not located in the same place as the Galaxy you see here's a bunch of galaxies but the gas is displaced over to the right here's the other bunch of galaxies and there's this shock front here and the gas is displaced a little bit to the left what happened is not too long ago cosmologically speaking these two clusters collided and went through each other the galaxies are just like test particles they just went right through but the gas didn't go right through the gas in one cluster smacked into the gas in the other cluster the shock wave was formed and both of the Globs of gas were stripped from where the galaxies are so most of the ordinary matter in the bullet cluster is not where the galaxies are it's where that gases which is in a different place this lets you ask the question is the gravitational field in the bullet cluster due to the ordinary matter or is it due to something else if you don't believe in dark matter you can believe that gravity falls off with a different Force law but you still need to believe that gravity points in the direction of The Source gravity points in the direction of where the matter is so if you believe in modified gravity as an explanation that would get rid of dark matter the gravity should be where the red stuff is not where the galaxies are now you can use your gravitational lensing trick to figure out where the gravity is you can look at the tiny distortions of galaxies in the background of the bullet cluster to map out the gravitational field and here it is you find that the gravitational field of the bullet CL cluster lies smack on top of where the galaxies are the ordinary matter doesn't there's a clear displacement between the gravitational field and the ordinary matter this is exactly what you would expect if most of the gravity in the cluster is caused by dark matter by Dark Matter particles that do not Collide that have no dissipation when the two clusters go through each other not only are the galaxies going through each other but the Dark Matter goes right along with them so the galaxies and the dark matter are sitting right there that's where the gravity is the matter the ordinary matter the hydrogen and the helium is sitting somewhere else it is impossible to explain this purely with a theory of modified gravity unless you have a theory of modified gravity that is smart enough to have the gravitational field point in the direction of where the matter would have been had this Collision not happened and then I would worry about you for other reasons this is not to say that Einstein is perfectly right in every way but what is to say is that dark matter really does exist the only way to explain this picture is to invoke invisible collisionless particles then there's many more of them than we can account for in the standard model of particle physics and you call that dark matter so again gravity could be modified and that could be interesting for Galaxy sized phenomena but dark matter really is there we're not going to get rid of it by by changing the law of gravity what about Dark Energy we can still move on to Dark Energy in we should be more hopeful when we approach Dark Energy because we know less about dark energy than we know about Dark Matter knowing less about something is always fun for theorists because we can invent a lot more theories that would fit the data what do we know empirically about the expansion of the universe as predicted by general relativity it turns out that the best test of general relativity as far as the expansion of the universe is concerned happens when the universe was one minute old we know what the universe was doing much better one minute after the big bang then we know what it's doing now in terms of comparing the stuff in the universe to its expansion rate and that's because one minute after the big bang was Big Bang nucleosynthesis the early Universe was a nuclear reactor it was turning free protons and neutrons into free protons which are hydrogen nuclei and helium nuclei with two protons and two neutrons each what happens is the early universe is hot and dense and nucleons are free when the universe cools off they can get together to form nuclei but at the same time as cooling off the universe is also getting less dense and the collisions happen less and less frequently so you need to know precisely the way in which the universe expands in order to predict the ratio of helium to hydrogen and other Light Elements like dyum and lithium it turns out that there's a prediction this is a picture of the size of the Universe versus what the expansion rate should be according to general relativity the R curve is the prediction of standard general relativity Lambda CDM means Lambda for cosmological constant CDM for cold dark matter you see the slope of this curve changes a little bit from the very early Universe when its radiation dominated to the middle-aged Universe when it's matter dominated to the old Universe when its Dark Energy dominated the fact that we live right at the bump is a puzzle a scandal in fact I like to call it it's the fact that the dark energy and the matter are similar to each other in magnitude today a that no one knows how to explain if you have any good ideas let me know this set of little line segments up there are things the universe could have been doing between 1 second and 3 minutes after the big bang in order to give you the right Light Element abundances from big bang nucleosynthesis so what it's basically telling you is the universe had to be doing what Einstein said it was supposed to be doing not exactly you can deviate a little bit you can start off nucleosynthesis expanding a little bit more slowly than than Einstein predicts if and only if you end up expanding a little bit more quickly you can compensate but really the lesson here is not that there is a little bit of rle room it's that there's not that much regle room there's no way that the Universe was expanding much more slowly or much more quickly than Einstein said at Early times so if you don't believe in Dark Energy if you want to get rid of dark energy and explain the current acceleration of the universe by modifying gravity you need to modify gravity in a way that only kicks in recently only kicks in down here at this corner up here in the early Universe gravity was correctly described by general relativity so how do we do that there's a bunch of different ways but none of them are very good I have to say no I've invented some of them it's very hard to invent modifications of gravity that make the universe accelerate and yet are consistent with everything we know about the universe so here are three ways among the others that people are disc that are people are discussing uh actively these days one is called DGP gravity after Dali gabad daza and PADI who invented it and it's based on extra dimensions and I'll talk a little bit more about this another is called f of R gravity which just says forget about extra Dimensions take Einstein's equation in four dimensions and fool with it change Einstein's equation in a consistent way but a way that is different from the ordinary prediction the final way is called modified Source gravity in which you don't change the way the gravitational field oscillates you change the source of gravity in general relativity the source is energy the more energy the more gravity in modified Source gravity it's some nonlinear function of the energy so that when the universe becomes thinned out at late times it can change its behavior in the universe can begin to accelerate so I'm actually going to talk in some detail about the first one here dtp Gravity even though I helped invent the other two because dtp gravity has been around the longest and we understand its implications the best Al although still not very well this is a very young field things are changing very rapidly I'm just going to give you a taste of the kinds of things that are going on so here's the basic idea of dtp gravity which is uh a complicated idea but a nice one in the sense that is a model that was not invented to explain the acceleration of the universe but it does anyway it comes out as a bonus so you might know about the idea of large extra dimensions of space the idea of some extra Dimensions goes way back to collus incline uh similar in time not long after gen relativity was invented but everyone thought we don't see extra Dimensions we only see three dimensions they should be curled up and put at the plank scale or some unobservable scale that we won't notice them you can actually have much larger extra dimensions in the plank scale as large as a millimeter across a macroscopically sized extra dimension of space the reason why you don't notice it is because you can't get there the idea is that there's some brain some three-dimensional object embedded in a larger universe and all of the particles of the standard model are confined to live on the brain electrons photons quarks gluons Etc stick to this three-dimensional brain the reason you don't see the extra Dimension is because you can't get there and you say okay why can't the extra Dimension be infinitely big why do you say a millimeter the answer is the one thing you can't confine to the brain is gravity gravity is the curvature of SpaceTime it's not a force so if you have some object it will stretch out into the extra Dimensions so you can put the extra Dimension at a millimeter because A millimeter is the scale at which we have experimentally probed gravity if the only deviations from Newton's law of gravity are submillimeter they're hard to detect now Dali gabad and paradi came along a couple years later and took this as a challenge they said well if you can make the extra dimensions a millimeter across we will try to make them infinitely big and they succeeded in doing that so in their model you have one extra Dimension a bulk that is actually four dimensions of space and one of time the reason why you don't notice it is because gravity is much stronger in the bulk than it is on our brain it's a little bit counterintuitive but what happens is because gravity is stronger even though gravity does leak out to the brain it costs energy to leak out to the brain if you think about the gravitational lines of force emitting from the Earth or the Sun they take more energy if they go into the extra Dimension so they stick close to the brain as long as they possibly can and you get a situation in which gravity looks four-dimensional on small scales and only becomes five-dimensional on large scales the opposite of the conventional versions of extra Dimensions so in DGP gravity it's a very interesting experimental challenge you have something where there's a mass creating gravity close by the mass everything looks normal four-dimensional general relativity up to very very tiny Corrections on very large scales things look five-dimensional we don't notice that because large scales means bigger than the Hubble radius bigger than 10 billion light years outside our observable universe but there's also a crossover regime in between where things become interesting so it becomes an experimental challenge to test gravity in this very very weak far away regime where things might be different than general relativity so the nice thing about this is that in a separate paper Cedric defia asked himself what is the COS ology associated with DGP gravity this equation tells you the expansion rate of the universe according to general relativity H the hble constant squared is proportional to row the energy density you see that this has a feature if there were no dark energy in the universe as the universe expanded and dilutes Away Row the energy density goes to zero H goes to zero and you'll be in an unexpand Universe you just being in flat empty space time in DGP cosmology you get a modification of that equation a new linear term in h which has the consequence that even when row equals zero even if there's absolutely nothing in the universe there's a solution when H is not zero H is a constant and that counts as acceleration so you get a self accelerating cosmology and this was not put into the theory it popped out so that's very attractive to a theorist you try to explain one thing you come with a model to explain something else that looks good so You' like to test this Theory and we've been looking at ways to test it using other cosmological phenomena if you can fit the acceleration of the universe which dtp gravity somewhat can it's not a great fit but it's a pretty good fit what about other things that are governed by Einstein's equation you want something that is in the very very weakest regime of gravity because that's where DGP gravity predicts deviations from general relativity so what that means is the evolution of very large scale structures very late in the universe's history the very largest perturbations in the universe slowly evolve in very recent times and they evolve in a way that is sensitive to the theory of gravity that is governing them how do you observe these it's hard to actually take data directly about large scale structure on the very largest scales but the evolution of the gravitational fields on those scales imprints and isotopies in the cosmic microwave background so if DGP gravity is correct the gravitational field on the very largest scales will begin to grow anomalously on the very largest scales and will give you extra temperature and isotopies in the cosmic microwave background so this is a plot of cosmic microwave background temperature fluctuations as a function of angular scale you've all seen this plot before but usually it goes up and then down and wriggles again I'm only showing you now the very largest angular scales because that's what we care about the white points are data from the W map satellite the red curve is the prediction for general relativity for Lambda C CM you notice two things one is that it does a pretty good job of going through the data Lambda CDM fits the data pretty well the other thing is that if you wanted to be a stickler you would notice that for multipoles between two and 10 almost all the points are below the curve nine out of 10 points are below the prediction you would begin to worry that maybe on the very largest scales the real world has less temperature and isotropy than is pred predicted by general relativity at the very largest scales we can measure lals 2 that point is real and that is quite far away from the prediction and people do worry about this they talk about the large scale anomalies in the microwave background had it been the case that DGP gravity predicted that the temperature and isotopies on large scales were smaller than they are in general relativity that would have been great news the real result we think is that they predict that the temperature anisotropies are larger than general relativity predicts so there's good news and bad news here on the one hand the bad news is this is bad news for DGP gravity it doesn't quite fit the data as well as you would like but the good news which I really think is more important than the bad news is that we have a new way to test general relativity on the very largest scales by thinking about Dark Energy we've been driven to think about gravity in a more precise and quantitative way in cosmology which has given us a new test of gravity so the shot is the lesson for people who want to build satellites and observe things is that you can test gr by measuring the expansion rate of the universe using two complimentary kinds of methods one kind of method is purely kinematic just measure the scale factor of the universe as a function of time directly you can do that with standard candles like Supernova we already talked about you can do it with standard rulers something called barion oscillations what you're doing is you're just making this plot scale factor in the universe as aun function of time you're making that plot as accurately as you can that is one way to be sensitive to Dark Energy another way is dynamical probes sensitive to the scale factor but also the evolution of large scale structure in the universe what is the power spectrum of large scale structure according to the microwave background according to weak lensing how many clusters do you have in the universe as uh determined by counts of clusters at high red shifts there's an ongoing program to probe the dark energy using methods like this and methods like this the moral of this story is don't look for the one best way to do it do it both ways and compare if you infer different behaviors for Dark Energy using kinematic probes versus using dynamical probes what you will have found is evidence that Einstein was wrong evidence that you need to invent a modified theory of gravity this has been recognized by uh the dark energy Task Force t force was put together to figure out what the best way is to probe the dark energy the lesson is look at both kinematic probes and dynamical probes we'll learn something about gravity as well as about Dark Energy so to conclude I just want to sort of emphasize the very biggest picture that is that we are entering a new regime in science of experimental gravitation we've had general relativity hanging around for 90 years now we're probing it in a set of regimes where we had not had access to before so the very largest scales macroscopically we have big bang nucleosynthesis as a test of gravity we have gravitational lensing comparing the mass that you infer in a galaxy or a cluster via lensing and via the Dynamics of the cluster as a new way to test general relativity and now we've realized the evolution of cosmic structure compared to the growth rate of the universe is yet another test ofen relativity we also have more traditional astrophysical sized tests we can probe general relativity the solar system like the Cassini Mission does we can probe it right here on Earth by bouncing lasers off of the Moon it turns out that laser laser ranging of the lunar orbit has the ability to test DGP gravity right here in the solar system uh there are ongoing experiments to do this some of them have gotten in trouble because the lasers keep bumping into airplanes but this is something that is actually a very nice way to uh detect the celestial mechanics of the solar system in a way that pushes into a regime where gravity might be different and furthermore as people here at NSF know ligo and hopefully someday Lisa will be looking for gravitational waves from black holes and from neutron stars this is certainly probing gravity in this mesoscopic regime where we haven't detected anything yet finally on very small scales we can be sensitive to gravity on millimeter sized scales and below this has always been something we've been trying to do test Newton's law about 1/ r s but now we realize through large extra Dimensions through dark energy and through other new phenomena there might actually be some motivation for looking at the behavior of gravity on these millimeter size scales on the tabletops as well as looking for fifth forces forces that are like gravity but have the difference that they affect different compositions differently protons and neutrons feeling different forces will be the sign of something up above and beyond gravity and finally most remarkably you can go to a particle accelerator and test gravity part of the upshot of the large ttra Dimension idea was the idea that the plank scale the scale at which quantum gravity becomes important might not be this very high inaccessible energy where we think it is it might be one trillion electron volts where the large hyron collider and the tatron are probing right now we could make gravitons at a particle accelerator we could even make black holes at a particle accelerator this is by far not a guarantee it is not a sure thing but it is completely realistic there are sensible models in which you will create strong gravitational fields at the Collision point of the Large Hadron Collider starting next year that is certainly a very exciting prospect willing to keep in mind so here's where we are the best news is that something is happening the universe is not just made of the standard model of particle physics we have Absolut definitive evidence that something Beyond either the standard model or general relativi is out there and governing most of the gravitational dynamics of the universe the dark matter sector certainly exists there's room to play about what the dark matter is you could combine dark matter with modified gravity you cannot get rid of dark matter by modifying Gravity the bullet cluster and other pieces of data speak against that dark energy I cannot be quite as definitive about I think it exists the theories that we know run into trouble empirically but we're just at the start of inventing these theories on the one hand it's very hard to out Einstein Einstein on the other hand it's a lot of fun and if you win then you win big so it's a highrisk high reward kind of game the most important lesson is that 95% of the universe is something we've never touched something we have inferred from its gravitational field but not ever seen here in the laboratory we should not be sanguin about the idea that we basically understand it it's a matter of dotting eyes and Crossing teas we should be very open-minded about surprises and keeping probing this regime both experimentally and theoretically as hard as we can thank you [Music] [Music] a

Channel: ResearchChannel

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Length: 57min 49sec (3469 seconds)

Published: Tue Sep 16 2008