What We Know and Don't Know about Dark Matter - Neal Weiner

all good things so um so I was given very very loose instructions which I will take advantage of I was asked to talk about various aspects of dark matter of course one thing that's very nice fast these two schools that there are a lot of lectures about dark matter and so you'll be getting a lot of information from Mike sign about the acción Ruben si will be talking about new searches Peter Graham will be talking about very very light types of dark matters and searches for them so I'm going to try and set things up and give you sort of an overview of what kind of things going to model building for dark matter and some of the ingredients that people have started using with these days now I can't assume that everybody in here has taken a cosmology class and it's a very important thing to have a rudimentary working knowledge of cosmology to talk about dark matter because one of the critical things about dark matter is where it came from how it got to be where it is now and all those things so let me begin I'm going to start these lectures just by giving us a lightning review of cosmology if you want to do precision calculations of course you need better results that I'm going to give here but at least for the qualitative understanding of the ideas that I want to talk about I'll try to make this all self-contained so the first thing to know about the universe is that it is a homogeneous isotropic universe Lee so far right so you'll know this homogeneous and isotropic and in general relativity you categorize and understand the universes by use of a metric so you measure distances in the universe with some metric that tell it takes you from your coordinate system into some distances and because the universe is homogeneous and isotropic the metric that we have that can be describing this is the following where you write a time interval the s squared is minus DT squared plus a squared of T DX cubed so this isoh trophy is represented here that you can rotate this the X cubed in any direction you want and homogeneous and that there's no special coordinate anywhere in this universe and the only way in which this metric evolve is that there's this scale factor a out front which describes distances so how do you think about that what do you think about that is that you go into some time the universe t1 and you draw some box here and then as the universe expand that box will expand uniformly in every direction so this length will stretch out this length will stretch out this length will stretch out so you'll go from this box to this box and so the entire expansion of the universe can just be described by a scale factor which is changing with time okay and that is the critical thing to understand about the free bean robertson-walker cosmology is that forgetting about the fact that there are galaxies and galaxy clusters at leading order of the universe is totally smooth and isotropic and you can describe everything that's going on by a single function of time a of T which describes how the universe is expanding obviously since we have plenty of time even though we have a discussion section tomorrow please don't hesitate to interrupt shout out whatever you like my handwriting is terrible please tell me if you can't read something and I'll correct it so what I wrote there is this quantity H is the Hubble parameter and the Hubble parameter which is the logarithmic derivative of a or the derivative of log of a with respect to time is the quantity which is probably the most useful in characterizing what is interesting or not interesting in the universe and there are multiple ways of thinking about H and so let me just write down what they are because if you talk to an astronomer how they think intuitively about H is very different from how particle physicists will think about H so for an astronomer H is a distance velocity relationship all right so that is to say that if you measure a distant galaxy and you see how far away it is and you measure how fast it's receding from you at least for the nearby universe those two quantities are proportional to each other and that is codified as Hubble's law which is where this comes from but that's not actually the most useful way of thinking about this because even though you can write H as some quantity of kilometers per second per megaparsec fundamentally the Hubble constant is a rate it's an inverse time quantity and so what you should think about this also is that H is a time scale over which the universe changes qualitatively by order one now that precisely order one factor will be different whether we're talking about the early universe or the middle universe of the late universe but it's always for everything all the times that I'm going to be interested in it's always going to be some order one factor and so what that means is is that you calculate the Hubble constant or Hubble parameter it's not actually a constant you calculate the Hubble parameter and the corresponding time scale tells you the distance a the universe will double if length scale more or less so that box will go to that box in one Hubble time and lastly H is a distance scale I mean we're all relativists here so distances and timescales are the same thing but it is also a distance scale which is effectively the horizon size of the universe so this is effectively the size of the universe now again there's an order one constant out front of this that dictates what precisely I mean but since H inverse is the time scale over which the universe changes by order one it is also effectively approximately the amount of time the universe has been around and so it is effectively also multiplying that by the speed of light how big the universe is currently okay so it is how far an observer starting back in the Big Bang for getting that inflation for the moment starting back in the Cosley connected Big Bang then watch out and see a signal propagate so currently we have a universe our current Hubble rate is approximately 10 billion years inverse and that's about how far we can see up to order one factors and these are three very very different ways of talking about the Hubble constant and they're all very very important this one is of course very important for astronomy this one is going to be important for talking about equilibrium processes and this one is going to be important for talking about observed properties and structure of the universe questions about this so far so in a flat universe we have the Freedman equation which is that the Hubble constant is a PI over 3 Newton's constant times Rho where Rho is the energy density of the universe so that is to say that Rho is equal to Rho matter so that includes dark matter atoms gas of all kinds radiation where radiation could be neutrinos can be photons and any other sorts of mysterious radiation cosmological constant or dark energy the energy density that is associated with space itself and so on anything else and G Newton is pública of the Planck mass to the minus 2 which is approximately 10 to the 19 GeV as you know so so why does this matter this matters because this means that we can understand how fast the universe is changing by understanding what is in it so we talked about the cosmology of the universe we're going to talk about the different eras of the universal in the universe Adama nated by the cosmological constant or dominated by radiation or dominated by matter and these things are going to tell us how fast the universe is and what the appropriate time scales are so for a given row give an energy density row we characterize that row by an equation of state parameter W and that W is approximately the relationship between the pressure and its energy density so it's not my choice to have had a P and a Rho U so close to each other and come up in cosmology as much as they do but that's how it is so for any given fluid row or any different energy density row there's some equation of state parameter that relates to the pressure yes oh because really what it is is it's D by its D Rho by DP properly which usually has this simple expression but not always and you have situations where of course you can have situations where a given fluid on certain distance scales has a simple relationship like this and in other distance scales has an additional pressure that comes from the fact that you've got some quantum pressure or something like this so for all of our purposes it's like this but I have to say that this is not exact because if you take this as exact you might go off and do something dangerous right so so we describe a fluid by its equation of state parameter so you can look at the equation of state parameters of the different fluids and again up to this approximation a fluid will dilute in a fashion that is dictated by its equation of a parameter so if I start with the given energy density I let the universe expand that energy is going to dilute and you can tell how it dilutes by categorizing it with this equation stay for ammeter so for instance the cosmological constant has an equation of state parameter minus one so it's constant dark matter as an equation of state cold dark matter has an equation of state parameter zero so its energy density dilutes like a to the minus three and radiation has an equation of state parameter of a third so it's energy density that loops like a to the minus four and all these things make intuitive sense and I'm just asserting these you can derive them but they make it to ative sense because the cosmological constant is energy density associated with space so as the universe expands obviously you still have space so that energy density hasn't diluted dark matter you start with your box full of stuff as you expand the box you have the same amount of stuff in just a bigger box so a huge is like a volume so this is saying that the energy density and dark matter dilutes light volume and radiation well if I have a bunch of photons in a box as I expand that box of course the number of photons will dilute like a to the minus three but each individual photon you can think of it as stretching out to a longer wavelength so the energy in any individual photon will also redshift like 1 over a so the energy of a photon right just like 1 over a and the number density photons right just like a cubed so altogether you get a to the minus 4 so so what can we do with that well you can ask questions about what does the energy density in various types of fluids look like well the energy density in radiation goes like e to the fourth so this is kind of obvious energy density is energy per unit volume volume has units of energy cubed so the energy units of energy density is energy to the fourth if you're in a relativistic universe where you have no other units the only unit you have is temperature so radiation energy density has to scale like T to the fourth just dimensional analysis alone tells you that there's a factor of G which tells you how many different degrees of freedom you have and your radiation fluids spin space flavor counting and then there's a factor that relates to whether it's a for me on a boson but for the most part people do these proximate calculations you'll just say radiation density goes like T to the fourth and be done with it certainly I will for today for nonrelativistic matter if of course just the number density of the individual particles if I'm labeling here ky time the mass of that particle Chi and an equilibrium particle if you have a particle which is in equilibrium then the number density can be written like this Jen you've got some dimensional parameters out front you no longer just have temperature so the mass comes into play and setting the scale but of course the most important factor in determining the amount of of an equilibrium nonrelativistic species is this exponential the Boltzmann suppression which goes like e to the minus M over T with a chemical potential that can correct that so if you have some residual baryon number density or lepton number density or something like that but neglecting the chemical potential for a moment the number density goes like the characteristic energy scales times e to the minus M over T and that's of course just the usual Boltzmann factor that when you get to low temperatures it's very easy for particles to convert into energy but it's very rare to have a process that has enough energy to go back the other way so we're almost done with our lightning review so the temperature of a fluid of a relativistic fluid will scale like the scale factor 1 over the scale factor assuming that there is no entry production so assuming I just take a single fluid and I let the universe expand with it that the energy density of the temperature of that fluid is going to go like 1 over a the way you can think about that is that every photon again has its momentum and as the universe expands that momentum gets stretched out so all the energies in that fluid get redshifted like 1 over a so why is this useful this means that as the universe expand the temperature drops so for the most part we can use the temperature as a time variable properly we're using T inverse as a time variable so the universe starts out at a very very high temperature and as the universe evolves goes to lower and lower and lower temperatures so T inverse is increasing as you go forward and if you forget about entry production and a few hiccups along the way that's a very very good clock to use to keep track of the universe so during the early universe during the early universe the Hubble constant squared I know you can't read some of that but that's okay because almost none of it matters except for this final scaling which is that I can take the Friedman equation that I had before I assume that I've got some relativistic fluid in the early universe I have some number of degrees of freedom G star that's coming up all my different fermions and bosons and I plug it all in you factor things and what do you get you get that the Hubble constant is approximately equal to T squared over m Planck times the degrees of freedom to the one-half and the number of degrees of freedom in the standard model can go up to slightly more than 100 so so g star to the 1/2 can by ignoring it can give you give you an error which is approximately a factor of 10 but for the most part when you're doing just order of magnitude estimates in the early universe that's fine so H equal to T squared over N Planck is usually a pretty good approximation question great okay so that is the early universe so you can write draw a plot of energy density versus time and you can look at the different components of the universe and you can look at how they evolve so if you go way back in time the dominant component of energy density was radiation it drops like T to the minus 4 then you have cold matter nonrelativistic matter it scales like T to the minus 3 because it's diluting like scale factor and scale factors starting T to the 4 to the screen its scalar like C to the 3 and then you have dark energy which is constant and you have these critical moments in the history of the universe we're about here so we've only recently had this transition where dark matter got overtaken by dark energy but there's this earlier period here which is what we refer to as the temperature of matter radiation quality that had comes at a scale factor of about 3300 or one over 3300 per egg and a temperature of approximately one electron volt so if you go to temperatures by which I mean the photon temperatures of the universe you go out you look around you there's the CMB I can take that CMB I can go back in time and ask what its temperature was and if I go back to the time where the temperature of that CMV was one electron volt prior to that time the universe was dominated by radiation and after that time the universe is dominated by cold matter so that means that the Hubble constant in the early time period is going like T squared and in this period of time the Hubble constant is going like T to the three-halves so that's all homogeneous that's just a smooth universe expanding and that this is the quantities that dictate for us how fast it's expanding and we can use to compare with other time scales questions about okay then the last thing that I will do in the lightning review of cosmology almost is to make one deviation from the smooth universe to say that the universe is not smooth but it's characterized by perturbation which we can call Delta which is the deviation from the average energy density divided by the average energy that's it yes that's right it's an accident it's an accident so so that's a very good point and we'll come back to that in a little bit so recombination happens at a temperature of about 0.3 EB at a redshift of between about around 1200 and there it's it's for our purposes and for you know the fact that they're so close together it's just an accident maybe there's some you know deep underlying anthropic reason for us that I will not be getting into but if Mark point of view it's an accident but it's a very important accident because the fact that there was a period of time before recombination when the universe was dominated by cold matter is is very important and we'll mention that in just a minute but for our purposes this is just an accident so whether you thing which is a good point not to scale is that right here if this is one electron volt then here at point three electron volts you have a process by which electrons and protons go together and form you two hydrogen and when they form neutral hydrogen that's the redshift at which we observe the COS of microwaves occur okay so the universe is characterized by perturbations Delta Rho over Rho so Rho is the average energy density of a given fluid any given time and Delta Rho is the perturbation from that and what we observe is that there are primordial perturbations in all fluids that we've observed at all scales and that they are scale invariant so that when you normalize this in a scale invariant fashion the size of fluctuations you see at on 1 Giga parsecs scale are the same as the size of fluctuations that you see on one mega parsec scale at least the initial perturbations were the same now that's not exactly right there's a slight running of the power as you go to smaller scales but it's very very close to a scale invariant spectrum and if you are in a radiation dominated universe then the energy density in dark matter in a cold matter fluid will scale grow like the log of a while is in matter domination Delta will grow proportional to a I'm not trying to get very technical about this point but all I mean is that if you start in a universe that has a little bit of extra matter in some place gravitationally that will draw stuff into it and as it draws into it that over density will tend to grow during radiation domination those over densities grow very very slowly during matter domination those over densities grow much faster and that's going to be very important okay last point on cosmology which is not even about cosmology it's really just about thermodynamics as I said the way we think about the Hubble parameter is it is a time scale and it is a time scale the quirk that characterizes both how long the universe has been around and how fast it's changing so it becomes the figure of Merit for comparing any other quantity that you have yes so I say that again oh these are perturbations of dark matter these are perturbations of only cold matter are growing like this during radiation domination so during the universe when you have radiation domination dark matter perturbations will grow like this but the radiation dot perturbations are not going to grow they they will oscillate as they do as a pressure food so then the perturbations will actually stop growing so the critical comparison is if you have some process characterized by a rate gamma then you have the question use gamma bigger or less than the Hubble rate and you can imagine a process for instance a neutrino and antineutrino annihilating into each plus t- in the early universe and you can ask the question is this process in equilibrium or is it not in equilibrium so to figure out whether this is an equilibrium process you would do the following you would say well I'll look at the number density of neutrinos I imagine I'm this neutrino I'm flying through the universe I'm going to scatter on some background neutrino so that's proportional to the number density of neutrinos with some cross-section times velocity Sigma be and this whole thing since this has to be a Z boson here is ultimately proportional to G / mu squared and then since I'm in a relativistic environment then the only way that I get my dimensions right is by putting a T to the fifth year so overall the rate for neutrinos going through a Z boson into e + u - you can estimate as just being G Fermi squared T to the fifth and you want to compare that to the Hubble constant which is T squared over n play and the critical point is that because they have different powers of T this process is going to be very very big in the early universe and then as time goes on it's going to get smaller and smaller and smaller until eventually this takes over so you can set these two things equal and find the temperature which of this transition happens and you find that it is around the MeV scale so this is the kind of I'm just sketching this out causes of the process that we know happens in the real universe that happens with the the particles in the standard model which is you ask a question are neutrinos in equilibrium with the electromagnetic background so photons can be in equilibrium with electrons and electrons can be equilibrium with neutrinos so when did that happen but what this tells you is if you go to temperatures above an MeV then the neutrino annihilation rate into electrons will be higher than the Hubble rate so that means that there'll be at least one annihilation in every Hubble time so on average a neutrino will not last a whole Hubble time before denial so that will tell you this is an equilibrium process I'm not trying to dwell on this too much except to say this is the kind of process this kind of calculation that one does quite a bit of and just checking to say is this an equilibrium process or not you estimate the process you compare it to the Hubble rate and see whether larger and four what parameters I should add that there are multiple types of equilibrium there's coarse chemical equilibrium where particle number can change and kinetic equilibrium where particle number won't change but you can maintain temperature between fluids and the difference between those is important and will come up later so good that's everything I need you to know about cosmology for the purposes of this lecture I hope you have taken moment and just internalized it good now we will use it not right away but we will be using it okay so what I'd like to do in this lecture is I'd like to talk about what it is that we start off by talking about what it is that we know about dark matter what it is we don't know about dark matter the way you might think about this is if you have the title of lecture or something like so let's suppose you want to build a model of dark matter okay where do you start what do you need to know what do you have constrained by and the thing that I would emphasize is that right now we really know lots of negatives so that when you're writing constraints when you're writing down models of dark matter you're trying to make sure that certain processes are less than something that lifetimes are longer than something and so on and so forth you know lots and lots of negatives about dark matter you know very little in the way of positives about dark matter okay so you're usually just trying to avoid constraints the second point that I want to make is that we know absolutely nothing at the moment about what dark matter is I want to really emphasize this if you if you think about this if you go back in time the way people have thought about dark matter has really evolved quite a bit if you go back to the 30s before many people would have thought dark matter was a silly idea like why is there dark matter we see all the matter you know sure there's some stuff that's not luminous but you know there's no need for dark matter and then they started seeing gravitationally that there's evidence for dark matter but they assumed that it's you know ordinary atoms and gas and then after more day to come in then it's clear that it can't be ordinary atoms and gasps maybe it's neutrinos and then everybody was on the neutrino bandwagon and everybody considers everything else to be exotic and then after a while it seems like neutrinos don't work but everybody is very into supersymmetry and you'll read papers where dark matter and neutralino are used synonymously and now we're moving past that but the point is that at every single point in time in our history people have had a lot of confidence in what the most likely model of dark matter was and every single time we've had a lot of confidence we've ended up not being right so people like me or you know Nate or Mike will get up and say to you you know here are this great model of dark matter you should be incredibly skeptical of us because it's really just what we're familiar with what we get used to biases quite a bit not not you Michael oh good so all I need to say is that our idea to a dark matter our change and so if somebody says to you Oh dark matter doesn't really act like that that would be very unusual for dark matter you should be very skeptical of that who's to say what dark matter should act like be very very skeptical of any sort of positive statement of what ordinary dark matter looks like so what is the evidence we have for dark matter these are the things that you need to absolutely satisfy first twiki and the Coma Cluster in the 30s sweetie observed the Coma Cluster so for those of you who do not do cosmology this is a cluster these are all galaxies and they fly around in all sorts of random directions so you can go and you can look at this cluster and you can measure how fast these galaxies are moving you can assume that the system is V realized so that is that the characteristic kinetic energy of any one of these galaxies should be comparable to its potential and you can then use this to infer the total mass of the system by how fast these galaxies are moving right so if they're moving very very fast there has to be a lot of matter if they're moving very slowly there has to be very little matter and from this the inference was that you needed 10 times more than observed more than the luminous map and even that was an underestimate so right you go out you count the galaxies you know how much a star weighs because we have a star you look at how luminous these galaxies are you figure out how many stars they need that tells you how much mass is in the luminous matter in the stellar matter that tells you how much mass you see you calculate their motions that tells you how much mass there is and you compare the two you find out you need a lot more mass than you observe now that's not a crisis of course because there's lots of mass that we don't see all right you don't really see planets you don't see very cold gas back then they didn't see hot gas there are all sorts of things that you cannot see but that's the first step where you actually need some matter which is not luminous the game change comes in the 70s where via Rubin and collaborators looked at rotation curves of galaxies so so here is your galaxy okay the spiral galaxy is rotating and you can measure the velocities at these points and then you can find distant systems here and measure their velocities as well so everything is orbiting around some central potential and you can make a plot now if all the mass is concentrated with the light then as you move farther and farther away Newton's law tells you the force should drop like one over R squared and if the force is dropping then of course the acceleration is dropping and so the V squared over R is dropping so you expect a curve that looks something like this so that is expected and what was observed was more like this and importantly that includes these objects which are way out here so what that's telling you is that the only way that you can have these objects continuing to rotate with these velocities is if there's a lot of mass around here that you cannot see and so that's the first really strong evidence for dark matter as we think of it now because if unlike in squeaky's case where it could have been matter distributed more or less ordinarily here this really can't act like stars it can't just be unexploded stars or planets or anything like this you have a type of matter which is really distributed in a way which is fundamentally different from how the observed luminous matter is distributed so as time has gone on we've now gotten tremendous new pieces of data let me emphasize three more one of them is from lensing so as we said before you have your galaxy cluster okay and you have your observer over here and then you can add some distant galaxies and the light from that distant galaxy can the lens can be bent as it comes around the cluster in between you and the galaxies and that lensing can be a strong lens where you actually really bend things coming through different paths or it can be something where you simply distort the image slightly and you need to infer its presence statistically but lensing has become a very very powerful tool for measuring the presence of mass between us and some distant objects so you can use this a means to make measurements of the masses of individual galaxy clusters and of course the most famous example of this is the bullet cluster the bullet cluster where you started with two clusters clusters tend to have a lot of hot x-ray emitting gas in their centers we believe that the dominant amount of mass is in the form of those in those hot x-rays x-ray meeting baryons so you started with one cluster coming this way in one cluster coming this way what happens is that the gas collided when the glass guest collided the gas slowed down but the mass continued to move on so you have some amount of mass that you can infer gravitationally and then some mass that you can infer from its x-ray emission they collide and the x-ray gets slowed down by the collision whereas the overall mass continues on now of course we did not observe this process this process happened over an extremely long time scale really we just observe this where we see these two x-ray emitting spots and we do a lensing map to infer the presence of dark matter but the critical thing from this is that it is the first example of a system where the center of mass and the center of baryons have actually been separated from each other and that's a very strong constraint on models of explaining dark matter through things like modify dynamics because you need to have a system that can actually separate the dark matter from the luminous map next is this growth of structure so as we said before the universe is full of these density perturbations Delta Rho over Rho and those perturbations should grow and you start with a small perturbation and it should get larger and larger and larger and eventually it becomes the galaxy that you observe today or something like that and you can do this in a variety of ways you can study the growth of structure and variety of ways one of them is with the CMB which of course has the famous what the other is by looking at the dimensionless power spectrum which is something like is Delta Rho over Rho squared and and what you can do is you're essentially going out and you're making measurements of the universe counting galaxies and asking questions like in a volume of the universe if I look at the universe on say Giga parsecs scale how large is Delta row of a row and as I move to smaller and smaller scales how large is Delta row of a row and what you see is that this increases and then turns over for reasons that are related to matter radiation quality but this is a prediction of your dark matter model or your cosmology because you start off with some primordial perturbations they grow in some fashion you go out you compare to what you observe in the universe and and you make a quantitative comparison this is most pronounced in the context of the CMB and the reason for this was this point that was brought up earlier so let's take a step back as we said over densities in the universe when you enter matter domination grow proportional to the scale factor okay so the grill proportional to a whereas in radiation domination they grow proportional to log of a so it's a very very very very slow growth of these perturbations and then matter domination happens and they start growing very rapidly but that's for dark matter dark matter is cold and collisionless so if it's got a gravitational potential it just likes to fall into it baryons are very different in the early universe baryons are interacting with the photon bath right protons and lectrons live electric charge so when you try to force protons and electrons into an over density they push back they have pressure so since we have matter radiation equality is it approximately 1 evey and recombination is approximately 0.3 you have this period of time in the universe where perturbations in dark matter can grow the perturbations in baryons cannot and so if the universe were actually just some exotic form of protons and electrons its Wurm would not be able to start growing until all that matter had become combined into hydrogen so structure would not have started growing in the universe until 0.3 Eevee and these plots would be very very inconsistent with the data ok so this is something that has to be bei very importantly taken into account the thing about dark matter models is that at one evey it really was already acting like dark matter okay it was cold collision with matter that was forming into over densities if it was made out of protons and electrons that could not have started happening until significantly later now I draw this plot here and it's not so important for you to understand exactly what I'm drawing like I said this is a measure of over density as a function of scale so very very large distances in the universe where there hasn't been a lot of time for the things to grow there's a certain amount of over densities as you go to smaller and smaller scales the average over density gets larger and larger and larger until you get to around 100 mega parsecs that around a hundred megaparsecs then normalized in this way that turns over and this is around ten mega parsecs is the distance scale at which Delta R over Rho is approximately 1 that's sort of where the universe begins to become nonlinear so in this regime here the universe is very very nicely linear and things can be calculated either with fairly straightforward tools or with more sophisticated tools and on your precision as you go to distances which are smaller than 10 mega parsecs then if you come harder and harder and harder to calculate these things so when you get down into this region of the universe where people actually don't use galaxy surveys that people use lyman-alpha systems to measure the average over densities it becomes very nonlinear and it becomes very hard to constrain so we know that dark matter was clustering like dark matter at a temperature of 1 evey but it actually because this looks like it was working even better than than that it was actually clustering well prior to money B and I'll talk about that in a little bit last constraint it tells us that dark matter is actually out there isn't really constraint on the existence of dark matter but it constrained on the absence of additional baryonic matter which is of course BBN Big Bang nucleosynthesis so you can go out and measure the abundances of lithium helium hydrogen deuterium and you can go and you can take your favorite code and you can run it and see how much an ordinary universe would have predicted for how much of those same elements there should be and all this is dictated by a single number which is the baryon two-photon ratio and we now notice the berry on the photon ratio is about six times ten to the minus nine if it had been much larger than that or much smaller than that then the abundances that we would have gotten are very very different but importantly we now have measured this variance Poisson ratio independently from the CMB and if you take this this turns out to tell you that Omega baryon which is the energy density in the baryon divided by the total energy density in the universe is approximately 0.04 so if there is dark matter it should be something other than protons neutrons electrons and so forth questions about this yes so the question is does 0.4 this one yeah this one complaint can constrain the dark matter self coupling it does I'll come to that in a second it's probably not the biggest constraint on that usually but this can all be understood by the fact that dark matter is a non interacting fluid so as you turn on interactions then you start needing to deviations from this and there's actually a fairly recent paper by C Racine and collaborators and I can find that and tell you the precise things where they put constraints on the size of dark matter interaction precisely from looking for those sorts of dark acoustic oscillations and they find that there's a constraint that whatever Fermi constant if you will dark matter farming constant should have a scale which is something larger than about MeV ish Dena meter slips like smaller than like 1 over mu V squared approximately except for they do find that there's a particular point in parameter space where maybe the fit is better than if you have none at all but it's better if you want to go there we'd go there are offline rather than me saying it here okay so so that's all the evidence there is for dark matter not all the evidence that's the dominant set of evidence for dark matter the reason why I wanted to point that all out is that all these pieces of data are from very very different environments right the CMB is from when the universe is about 300 thousand years old when the universe has a temperature of about 0.3 Evie and perturbations are very very linear galaxies and lyman-alpha systems go from both linear to nonlinear regime but involve the integrated properties of the universe over the history of the universe lensing is a totally different technique that allows you to measure the mass of objects out there rotation curves are a sistah size that smaller than lenses and of course BBN is a completely orthogonal measurement from all these about what types of matter there are on the universe and the reason why it's worth noting that all is that dark matter is not a single piece of data right and if you go out and you talk to your average person on the street they will probably point the rotation curves as being the best piece evidence for dark matter but in reality there's evidence for dark matter all throughout the history of the universe from a variety of experimental II independent techniques and they all point to the same idea that there is a significant amount of dark matter in the universe about six times more abundance than ordinary matter okay so at this point it's worth noting that this is the conservative option right it's not the conservative option to say oh well maybe Newtonian dynamics is modified maybe Newtonian Maat dynamics is modified maybe that is the explanation but that's not the conservative option the conservative option is there's just some stuff that you can't see and you want to find out what it is questions so so that's the evidence for dark matter so what do we know about its properties what are the constraints on it so like I said before it's mostly negative at zeroth order we know that it's massive ie that it actually has some sort of energy to it and that its mass is like mass not like radiation so that it has an equation of state which is very close to zero so it's nearly pressureless there is a an idea which is the in cosmology that people like to talk about which is the comoving horizon size which is to say that you can take a scale today and ask what that equivalent scale was in the early universe right so you can talk about the megaparsec scale at any time in the early universe even though it was much smaller than and so what you can ask is as I go down to the smaller and smaller and smaller scales where I've observed dark matter perturbations what's the smallest scale that I've currently observed that and how big was the universe when that was the entire universe right so I can say go back in time and say I see I see galaxies now that are say 100 kiloparsec in size how far back do I have to go in the universe when the entire horizon of the universe was that okay even though it was contracted and the answer to that is that the objects that we observe came inside the horizons that is what you say they came inside the horizon these modes came inside the horizon at temperatures of about ke V so if you go back to temperatures higher than a ke V the horizon size is very small and the parts of the universe that are inside those patches of the universe are smaller than the scale that we can currently test Dark Matter on when the universe was about hey Evie you had regions of the universe that have now turned into structures that we can observe therefore starting at about a ke V Dark Matter better have been acting like Dark Matter so when I say the Dark Matter is massive and approximately pressureless I mean that it is massive and approximately pressureless today and that it had better been approximately pressureless ever since ke v prior to the ke V I can't actually say very much about how dark matter was in parsecs this ends up being it's much smaller than mega parsecs this ends up being kiloparsec well let's okay let's we can talk about that we get out rather than a so-so all dark matter is cold all dark matter that explains the structures that we observe today is cold today when people make a distinction between hot dark matter warm dark matter and cold dark matter it's actually a little ambiguous what that means but typically it means what the characteristics of that dark matter were within experimental ranges of validity or when it was formed or something like that so for instance take the extreme example of neutrino dark matter which is the sort of quintessential hot dark matter model if you have a neutrino which is 0.1 evey in mass let's just say which is approximately okay with roughly the same as what you went for the long baseline experiment then the neutrino became nonrelativistic at V of approximately a hundred or so okay so yes it's hot dark matter in that when it was around earlier it was hot and it free streamed and smooth things out but well before now it became cold so what I'm saying when I say that it's massive and cold I mean that the dark matter is massive and cold today and it is the massive and cold ever since temperature of a KUB and later warm dark matter is then characterized as being right on the cusp essentially where it had temperatures at ke D that were around at ke V and so right where we're starting to lose the ability to discern these structures it was starting to smooth these things out and that's useful then for trying to change structures of observing galaxies deplete some sub halos smooth out some cuts but all dark matter that is the dark matter so if you assume there's only one type of dark matter all dark matter models that explain the dark matter are cold today and has been cold since about ke D so the next thing is that dark matter these are all zeroth-order things should be neutral neutral I mean electrically neutral and so let me just talk about two different possibilities for that and the constraints on them so the simplest possibility is you can imagine the Dark Matter actually carried some electric charge and if it carries some electric charge then in the early universe it would actually be tightly coupled to the photon and barium plasma as well so as we said baryons can't start growing their density perturbations until recombination because they're tightly coupled to the photon path and if dark matter had an electric charge it would also be tightly coupled to that same photon bath and it would not be able to grow its perturbations either so you need the charge to be small enough so that dark matter is not tightly coupled and there's a paper but it's a little confusing to read just because it was written a long time ago and things have not dramatically changed because this is a qualitative statement by Duvall ski gorbunov and boots off from way back in ancient history back before there were dots and archive numbers and they basically found that if you make a plot of charge and mass you're cited at nav here's 10 to the 14 a V and here's 10 to the minus 6 of the electron charge and here's 10 to the minus 5 the electron charge that something like that region is ruled out the reason why I have drawn this plot in this funny way is that there's actually in there flawed a lot of additional information in here that's not really relevant for us anymore but you can see that even for very very small couplings very very small charges dark matter becomes tightly coupled to the photon that if you have a lighter dark matter particle it becomes tightly coupled more easily and thus it's really matte the other thing in terms of charge dark matter that I just want to comment on is that you might have the idea of because lots of people had this idea is well maybe the final particle is not charged but maybe there's a very very very massive thing like a proton that it weighs like a tev and it has an electric charge and it binds together with something else it's like a very very massive electron and they make a neutral object even though the constituents are charged ok but let's suppose they bind together from electromagnetism not from like strong interactions not like neutrons but like you really have a TV mass proton and a TV mass electron of a bind together that is also ruled out from something called heavy hydrogen searches so you can go out and you can get water which is made that's a lot of hydrogen and you can look at it to see if any of the water molecules contain within them heavy hydrogen because if you have these TV mass protons and TV mass electrons occasionally they will bind with a ordinary electron and that ordinary electron will chemically interact just like hydrogen and it will form water and such things and so the constraints on this is that the abundance of this so the fraction of ordinary hydrogen which is in the form of heavy hydrogen is less than about 4 times 10 to the minus 14 for something that's sort of heavier than ordinary hydrogen and less than about GeV and I just bring that up not because this is the model constraint that you're going to most run into but just to emphasize that there are when you start thinking about any specific model oftentimes these very very precise studies these precision searches that have gone on that can constrain what you're talking about yeah so literally color charged literally color charge yeah so there's a type of dark matter that's called quirky dark matter that functions like this that is more or less fine as long as you understand its thermal history well and colored particles have a very confusing thermal history but but as long as the object itself combines to a neutral object that cannot bind with an electron this is fine you have to make sure that the object that you're talking about has its lowest energy state such that it is actually electrically neutral and doesn't have approximately degenerate things like the cosmology I'll just say the cosmology of it depends on how massive your particle is and if your particle is very very heavy then it largely looks very wimpish if you're tryna make something lighter then the cosmology becomes much more complicated yeah yeah but I'm assuming that we're going to put it in a mass scale where it's not gonna mess with that yeah I have to think about what the actual limits are on how light that can be yeah that's the abundance that's the that's the the fraction of hydrogen which is in the form of super-heavy hydrogen for this mass ratio that's right if it's lighter than this and they're not very good at finding it so right okay so dark matter is neutral it is cold and it is non interacting so when dark matter is non interacting what does that mean what that means is is that at current levels of simulation two leading order dark matter that does not interact at all is in good agreement with the data and we can have arguments about that about Korres and cusps and dwarf galaxies things like that but a leading order a dark matter particle that has zero interactions is fine therefore when you turn on interactions you basically start running into problems if not immediately then very very quickly on the order of magnitude type plot so the leading analysis that you do is just ask the question how large do I have to be before I start getting any sorts of interaction so you pick your favorite system you find the number density in that system you find the velocity of the particles met system you asked how long that system has been around so for instance you take the Milky Way galaxy you measure how much dark matter is in it you look at how fast things are moving about 300 kilometers per second how long has been around about as long as the age of the universe and you set that equal to 1 to get a cross-section limit and the cross-section limit that you get from lots and lots and lots of of different of different systems is is this that the cross-section divided by 10 to the minus 24 centimeter squared is less than the mass divided by TV the way people like to talk about this is that the cross-section per mass is less than about one centimeter squared per gram that's how astronomers talk about it these numbers end up being about the same and it's actually quite it's quite remarkable that you end up with very very similar limits from many many systems dwarf galaxies clusters of galaxies the one that people will point you the most is if you look at the bullet cluster when these two clusters collided with each other if there had been a large amount of scattering then the Dark Matter halos would have slowed down as well and that ends up with a limit which is about a factor of two stronger than this if you convert this into just natural units this ends up being about 100 MeV to the minus 3 so I'll just make a note of that now because that will come up later as a relevant scale the other thing that I'll say is that these different systems have different velocities so dwarf galaxies tend to be very slow clusters tend to be very fast and so you come and you have a hard limit like this from the bullet cluster where particles are moving at a few thousand kilometers per second those limits would not necessarily relevant inside of Milky Way so so when people say that's the limit on dark matter cross-sections that's really the limit on dark matter cross-sections in system and if there are clatter has a velocity dependence to its interaction then Bend those can be easily abated to last things what about force you might ask whether dark matter can have an additional long-range force and there is a paper by Tenzin and Tammy Kalki actually didn't write down the year so the idea is what if dark matter had interactions that bound it inside of the galaxy that were different from ordinary gravity and they found that the strength that they call B which would be less than 0.2 which is to say that the coupling of dark matter to a scalar should be less than 0.2 of gravity and the limits come from the fact that if you look at dwarf galaxies that are orbiting around our galaxy those dwarf galaxies have dark matter in them and darion and if the dark matter and the baryons had different types of interactions then they would actually orbit at different rates you'd have an equivalence principle violation and you'd either and you get a separation of the dark matter from the baryons and you'd lead to a stream of baryons falling out of the Dark Matter halo the absence of those led to this limit now I don't know that I would necessarily hold this number completely rigorously but certainly order one deviations to gravity can lead to changes on the Galactic skills and the last constraint is that they should be stable right so dark matter people talk about cold collision with dark matter it should be neutral it should be cold it should be dark and it should be here so it has to be stable but how stable the most recent analysis I know of this is in this paper where they looked at what happens if dark matter is decaying into invisible particles the dark matter decays into electrons or photons or protons there are all sorts of limits on that but a dark matter just decayed into something invisible which meant that as the universe was expanding dark matter was actually diluting a little bit more rapidly than it should have been then you can see those effects on cosmology and they put a limit which is at the fraction of decaying cold dark matter time the rate of decay and cold dark matter should be less than 0.086 cleanse aged universe so if dark matter is decaying it better have a lifetime which is longer than about ten times the age of the universe otherwise it will start having cosmological problems but at this set of requirements were pretty much ready to start building models of dark matter if dark matter has relatively small interactions relatively long-lived neutral and cold at least since ke B that's going to be an acceptable model of dark matter as long as you get the abundance right so I'm going to stop there and I'm going to stop there and we will pick up tomorrow with models of dark matter and I left some time for questions and I can also take questions after questions yeah

Channel: Institute for Advanced Study

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Id: NJhANpBtUyQ

Length: 73min 56sec (4436 seconds)

Published: Tue Jul 18 2017

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The IAS PiTP 2017 summer program schedule with links to the videos and PDFs for the various talks: https://pitp.ias.edu/program-schedule.

The theme for this program is "Particle Physics at the LHC and Beyond". The program runs from July 17 to 28, 2017. Many of the talks have PDF notes or slides for the talks. The program is open to advanced graduate students and postdocs.