1. Are we sure it isn’t ordinary matter/baryons? Not in compact objects (brown dwarfs, etc.) Baryons should also contribute to nucleosynthesis But we got it to work out assuming it’s not baryons Most likely: it will be some sort of undiscovered particle: X Particle must be stable or long lived (> 13 Gyr) Must be a reason particle did not disappear like electrons/positrons Assume there is a process that gets rid of X’s: At some temperature, this process must stop, or freeze out Freeze out occurs when  t drops below 1 Dark matter candidates are classified by how high temperature is at freeze out If particles are relativistic at freeze out, we call it hot dark matter If particles are non-relativistic at freeze out, we call it cold dark matter

2. Neutrinos as Hot Dark Matter We will first study hot dark matter The prototypical hot dark matter is neutrinos: Imagine if neutrinos have a mass There are three types of neutrinos: assume only one has a mass Neutrinos freeze out at about 1 MeV – we already know mc 2 is much smaller than this for neutrinos At this point, number of neutrinos is conserved – it cannot change The density of dark matter is: (Solution O) The mass of neutrinos we need is:

3. So what’s wrong with hot dark matter? The list is long We will focus on one aspect: structure formation Consider the momentum of neutrinos At freeze out, their energy is roughly 3k B T, and their momentum is p = E/c = 3k B T /c At the time of matter-radiation equality, this formula still works In the lifetime of the universe, at this time, a neutrino moves a distance Suppose at this time, there were a region smaller than this that had high density Neutrinos would simply run from high density region to low density Precursor to structure would get wiped out

4. What’s the size of the first structure? Any structure smaller than this will get wiped out Whatever structure formed first must be larger than this The amount of ordinary matter in a structure this size will be: This is the mass of a galaxy cluster Suggests clusters (or larger) were the first structures formed Evidence suggests globular clusters were first For this reason and others, hot dark matter, and neutrinos in particular, have been rejected as dark matter candidates.

5. What say experiments about neutrino masses? There are three neutrinos, which we will label 1, 2, and 3 We can’t see the masses directly, but we can measure differences in masses We also have decent bounds on the mass of the first one: It seems clear that neutrinos are not the dark matter Still, there are always crackpots that try to make it fit anyway:

6. Cold Dark Matter Suppose in the early universe, there were some species of heavy particle X Assume it is stable, by itself Assume it comes in equal parts X and anti-X It may even be its own antiparticle In thermal equilibrium, it should completely destroy itself: However, the last few X’s will have a hard time finding partners to annihilate with Typically, particles disappear when the temperature is about k B T F = mc 2 /30 Down from usual mc 2 /3 because we are trying to get rid of the last little bit When will annihilation stop? When:

7. The Annihilation Cross-Section Now, the dark matter has density that scales as a -3 And aT is roughly constant So  /T 3 is roughly constant Because particles have annihilated, it’s really  /g eff T 3 that is nearly constant For definiteness, assume g eff,F = 100 This annihilation cross-section needed no matter what the mass of the X is.

8. What is the Dark Matter? There is an approximate upper bound on the cross-section for any process involving particles of mass M: Cross section usually lower than this, but typically: This is right in the range for LHC, and for supersymmtery Cold Dark Matter is considered the leading contender for dark matter models Of course, there are always crackpots with other crazy ideas.

9. Advantages of Cold Dark Matter: It is heavy, and therefore slow moving This means any density fluctuations will not get wiped out There is no problem “packing them in” to galaxies, even if they are fermions It occurs at a scale where we soon should be able to discover it The cross-section is actually a pretty natural one for particle physics Density perturbations: What we will discover later Because they couple poorly to ordinary matter, they can start making structure as soon as universe is matter dominated Helps explain how universe is smooth at z = 1100, lumpy at z = 10. They end up naturally in more spherical “halos” around galaxies

10. Baryons are a group of particles including protons, neutrons, and some heavier similar particles There are also anti-baryons, such as anti-protons and anti-neutrons In the standard model of particle physics, baryon number is conserved: At high temperature, there are no baryons, instead there are quarks: Conservation of baryon number simply becomes conservation of quark number There is significant evidence that the universe contains more matter than anti-matter Solar wind and our solar system Colliding clouds in our and other galaxies Merging galaxies Colliding Galaxy Clusters Hard to imagine that somewhere there is anti-matter lurking p+p+ + n0n0 + e+e+ u + d + e+e+

11. Where did the Baryons come from? Could be part of “initial conditions” of universe Intellectually unsatisfying Inconsistent with ideas about inflation It could be created by some process in the early universe Assume started with equal numbers of quarks and anti-quarks Can be rather inefficient What do we need to create the baryons? We need a process that violates baryon number We need to be out of thermal equilibrium Decays satisfy this nicely The process must treat particles and anti-particles differently “C violation” and “CP violation”

12. How to make Baryons from nothing Suppose there were some heavy particle that decays asymetrically: call it X u u d X + u u X + – e+e+ u d X + X + – e-e- – – u – Provided C and CP symmetry are broken, these rates can be unequal This can lead to baryon asymmetry The problem: This can also lead to, for example, proton decay Experimentally, we have a limit on proton decay: d X u – e+e+ Rate for this process depends on mass of X:

13. What makes the baryons? Consider Grand Unified Theories: Has particles around 10 16 GeV or so Has baryon number violation! Has lots of C violation and (probably) CP violation Looks ideal for baryogenesis So many GUT’s, we have no idea which one is right Would help a lot if we saw a proton decay Super Kamiokande Neutrino detector and nucleon decay experiment Eventk B T or TTime Grand Unification/Baryogenesis10 16 GeV10 -39 s Supersymmetry Scale/Dark Matter created500 GeV10 -12 s Electroweak Scale 50 GeV10 -10 s Quark Confinement150 MeV1.4  10 -5 s