COSMOLOGY
Problem Set 5
April 26, 2010
Problem 1
: ΛCDM
Consider the standard ΛCDM cosmological model with Ω
M
= 0
.
25 and Ω
Λ
= 0
.
75;
you may adopt
H
0
= 70 kms

1
Mpc

1
. Assume that the current density in relativistic
particles (“radiation”) is Ω
R
= 8
.
0
×
10

5
.
a) Find the redshift of equal matter and radiation densities,
z
eq
.
[5]
b) Find the age of the Universe,
t
eq
, at
z
eq
. [5]
c) “Recombination” occurs for
z
rec
= 1100. Find the age of the Universe,
t
rec
, at
z
rec
.
[5]
d) Find the proper radial distance to the horizon at recombination,
R
H
(
t
rec
), in units
of the present Hubble distance
c/H
0
. [10]
e) Identify each of the horizonsized volumes from part d) with a comoving volume.
How many of these comoving volumes are today (
t
0
,
z
= 0) within one “Hubble
volume” (
≡
4
π/
3(
c/H
0
)
3
)? [5]
Problem 2
: Steady State Model (yet again!)
For the Steady State cosmological model it is
assumed
that the number
densities
of particles, photons included, remains constant as the Universe expands (and, in
particular, as the photons redshift).
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 Spring '10
 STEIGMAN
 Thermodynamics, Current, Energy, Radiation, Physical cosmology, steady state model, time Te

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