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

orXX e e XX e e

Neutrinos as Hot Dark MatterWe 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 mc2 is much smaller than

this for neutrinos• At this point, number of neutrinos is conserved – it cannot change

3

34 2

3Bk T

n gc

3

2

33 42

4 11Bk T

c

311 n 8 -31.12 10 m

• The density of dark matter is: (Solution O)31.27 u/md 3 2 2 31.27 u/m 931.5 MeV/u 1183 MeV/c /mc

• The mass of neutrinos we need is:dm

n

2 3 6

8 -3

1183 MeV/c /m 10 eV

1.12 10 m MeV

2 10.6 eVm c

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 3kBT, and their momentum is p = E/c = 3kBT /c• At the time of matter-radiation equality, this formula still works

3 Bp k T c 3 0.714 Bk T c 1.63 eV/c2

p pcv c

m mc 1.63 eV

0.1510.6 eV

c c

• In the lifetime of the universe, at this time, a neutrino moves a distance d vt 8 70.15 3.00 10 m/s 57,000 y 3.156 10 s/y 198.3 10 m

• 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

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:

198.3 10 md

343 mM d 334

03 1md z 3 319 343 8.3 10 m 1.53 u/m 3231

711.24 10 u 27

30

1.66 10 kg/u

1.99 10 kg/M

1410 M

• 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.

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

2 2 4 5 22 1

2 2 4 3 23 2

8 10 eV

2.5 10 eV

m m c

m m c

• We also have decent bounds on the mass of the first one:

21 2 eVm c

• It seems clear that neutrinos are not the dark matter• Still, there are always crackpots that try to make it fit anyway:

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 kBTF = mc2/30• Down from usual mc2/3 because we are trying to get rid of the last little bit

• When will annihilation stop? When:

orXX e e XX e e

1 t Fn v t 2

13

eff

2.42 s MeVF

B F

n ck Tg

eff

3 2 8

0.413

s MeV 10 m/sF

B FB F

gn

k Tk T

2

eff3 8 2 2

0.413

10 m MeVF

B FB F

gn m mc

k Tck T

7eff

3 2 2

1.24 10

m MeVF

B F

g

ck T

The Annihilation Cross-Section• Now, the dark matter has density that scales as a-3

• And aT is roughly constant• So /T3 is roughly constant• Because particles have annihilated, it’s really /geffT3 that is nearly constant

70

3 2 3effeff0 0

1.24 10

m MeVd

Bg cg k T

• For definiteness, assume geff,F = 100

37eff0 0

2 30 eff

1.24 10

m MeVB

d

g k T

g c

37 5

3 2 2

1.24 10 3.36 2.725 K 8.617 10 eV/K

1.27 u/m 100MeV m c

37 4 3 3

2 2

4.17 10 2.35 10 eV m

12.7 u MeV mc

40 24.6 10 m

• This annihilation cross-section needed no matter what the mass of the X is.

7eff

3 2 2

1.24 10

m MeVF

B F

g

ck T

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:

2

2

c

Mc

40 24.6 10 m

• 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.

22X

c

M

2 X cMc

1

100 1x 7

40 2

1.97 10 eV m

4.6 10 mX

1310 eVX

2 2 410 10 GeVXM c

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

• 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 numberThere 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++n0 +e+

u+d +e+

106.2 10Bn

n

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”

106.2 10Bn

n

exp Bp E E k T

How to make Baryons from nothing• Suppose there were some heavy particle that decays asymetrically: call it X

u

u

dX +

u

uX +– e+

u dX +

X +

–

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:

dXu– e+

0p e

1 331.6 10 y • Rate for this process depends on mass of X:

52

42100

p

X

m c

m c

1/ 452 2 1 11100X pm c m c

155 10 GeV

What makes the baryons?Consider Grand Unified Theories:• Has particles around 1016 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

Event kBT or T TimeGrand Unification/Baryogenesis 1016 GeV 10-39 sSupersymmetry Scale/Dark Matter created 500 GeV 10-12 sElectroweak Scale 50 GeV 10-10 sQuark Confinement 150 MeV 1.410-5 s