COSMOLOGY
Problem Set 7
May 10, 2010
Problem 1
: Another Sterile Neutrino
Suppose there is a new, very weakly interacting, “sterile” neutrino
ν
s
which does
not
mix with the usual (“active”) neutrinos.
The
ν
s
are light but not massless
(0
negationslash
=
m
ν
s
≪
1 MeV).
a) If these sterile neutrinos decouple at a temperature of 10 GeV, find their contribu
tion to ΔN
ν
≡
ρ
ν
s
/ρ
ν
, the effective number of equivalent neutrinos at
T
γ
≈
1 MeV.
[10]
b) Assume that these
ν
s
are nonrelativistic at present. In terms of their mass
m
ν
s
, find
the present value of their density parameter Ω
ν
s
0
. (You may adopt
H
0
= 70 km/s/Mpc
and
T
γ
0
= 2
.
725 K). If observations require that the upper bound to their present
density is Ω
ν
s
0
≤
0
.
23, find the upper bound to the
ν
s
mass. [10]
Problem 2
: Early Universe Neutron – Proton Ratio
In the early Universe the chargedcurrent weak interactions keep neutrons and protons
in equilibrium (“chemical” equilibrium) until (approximately) the weak rate (Γ
wk
)
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 Spring '10
 STEIGMAN
 Particle Physics, Electron, Mass, Neutron, Light, Elementary particle, proton ratio

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