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COSMOLOGY
Problem Set 8
May 19, 2010
Problem 1
: Dark Matter Candidate
Consider a spin 1/2, symmetric (
μ
= 0), massive fermion whose annihilation rate
factor is massdependent:
β
=
a
σv
A
= 5
.
0
×
10

21
/m
2
(GeV) cm
3
/s. For
m
= 300 GeV,
±nd:
a)
T
*
(and
x
*
).
[Hint: You will need to guess
g
eff
*
and fnd
x
*
. Then, using
this value oF
x
*
and
m
, you will fnd
T
*
From which you may estimate
g
eff
*
.
IF this value agrees with your guess, fne. IF not, you will need to iterate,
based on what you have Found, until you converge.]
[10]
b) (Γ
/H
)
*
. [10]
c) Ω
h
2
. [5]
particle mass which results in Ω = Ω
CDM
, where Ω
CDM
h
2
= 0
.
112.
[Note: AFter
you’ve guessed the value oF the mass, you can repeat parts a  c to check
your guess.]
[5]
Problem 2
: The Universe at the Epoch of Primordial Nucleosynthesis
a) Assume that the ratio of nucleons to photons in the Universe at present (when
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 Spring '10
 STEIGMAN
 Mass

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