Phys/Astro 228: Extragalactic Astronomy and Cosmology
October 13 2006
C.–P. Ma
Problem Set 5
Due in class Friday October 20
Readings: (1) Ch 2.4 of Dodelson; (2) All of “Dark Matter” from
Particle Physics Review
(linked at course website).
1.
Equality Time
(a)
RadiationMatter Equality
:
The correct answer to Problem 2(d) of Problem Set 4 is: the presentday radiation density is Ω
0
,r
h
2
=
4
.
15
×
10
−
5
. From this, calculate the equality redshift,
z
eq
, at which the energy density in matter
equals that in the radiation. (Leave Ω
0
,m
and
h
as free variables in your answer.)
Approximately how old was the universe at
z
eq
, for a model of Ω
0
,m
= 0
.
27, Ω
0
,
Λ
= 0
.
73, and
h
= 0
.
71?
(b)
Matter
Λ
Equality
:
For the same model (i.e. Ω
0
,m
= 0
.
27, Ω
0
,
Λ
= 0
.
73), calculate the redshift at which the energy density
in matter equals that in the cosmological constant.
(c) Make a simple sketch showing how the energy density in radiation, matter, and Λ evolves with the
expansion factor
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 Fall '06
 CHUNGPEIMA
 Cosmology, Particle Physics, Dark Matter, Energy density, luminosity density

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