Freeze out

Question 1

What happens in a radiation dominant era?

Answer 1

T/T_o = 1/a
Ignore matter, curvature and Λ

Question 2

How much energy is needed for electron and positron to annihilate and create 2 photons?

Answer 2

1 MeV

Question 3

When do particles form and annihilation happen freely?

Answer 3

when k_B T is greater than mc^2

Question 4

What happens when k_B&raquo_space; 2GeV

Answer 4

Annihilation (e.g proton and anti-proton) occurs as a two way process and 2 photons are produced

Question 5

What is the mass of a proton?

Answer 5

1 GeV

Question 6

What happens when k_B T ~ 2GeV

Answer 6

Annihilation of particles becomes a one way process
(this is the rest mass of 2 protons)

Question 7

What is freeze out?

Answer 7

Any process that becomes irreversible (one way reaction)

the photons are redshifting as the universe expands

Question 8

When does a reaction become electromagnetic?

Answer 8

When a photon is involved

Question 9

What does freeze out cause?

Answer 9

The ratios of types of particles in the universe

Question 10

What happens in freeze out?

Answer 10

Expansion timescale becomes shorter than reaction timescale

Ambient temperature is less than required to enable the reversible reaction

interaction rate < expansion rate

Question 11

What is the average time between interactions?

Answer 11

t ~ 1 / (σ n c)

Question 12

What is the reaction rate Γ ?

Answer 12

σ n c

Question 13

For thermal freeze out of any particle. when does annihilation occur?

Answer 13

k_B T ~ 2 mc^2

Question 14

What happens when k_B T&raquo_space; 2mc^2?

Answer 14

The particle is relativistic and they behave like radiation so the radiation density in the early universe includes relativistic particles

Question 15

What happens as a result of massive particles annihilating in early universe?

Answer 15

They leave either photons (CMB) or neutrinos

The present day radiation density includes all of these annihilated particles

Question 16

What does the fraction of electron and protons compared to annihilated particles show?

Answer 16

The fraction is insignificant and shows that present day radiation density is a close match to the redshifted density from early universe

Question 17

What is the last massive particle to become non relativistic?

Answer 17

Electron (and positron)

Question 18

What happens to electrons and positrons after weak reactions involving neutrinos which have frozen out?

Answer 18

Electrons and positrons annihilate as free neutrons are not stable

All of the annihilation energy goes to photons instead and temperature rises (photons and neutrinos have same temp up to freeze out)

Question 19

What is the weak interaction involving neutrons and neutrinos?

Answer 19

n + v_e <=> p + e-

Question 20

What happens to entropy in the early universe?

Answer 20

Energy is conserved so all of the electron and positron energy goes to photons

Question 21

When do neutrinos decouple?

Answer 21

T > 1MeV as weak reactions stop (freeze out)

Question 22

What does the differing temperatures of photons and neutrinos show?

Answer 22

ρ_v = 0.68 ρ_γ