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Phys/Astro 228: Extragalactic Astronomy and Cosmology
September 22 2006
C.–P. Ma
Problem Set 3
Due in class Friday September 29
Readings: Chapter 2 of Dodelson and Sec 19.2 of “Big Bang Cosmology” from Review
of Particle Physics (see link at course website).
1.
Age of the Universe
In class, we derived expressions for the age of the universe,
t
0
, in terms of the Hubble and the density
parameters.
(a) For Ω
Λ
= 0 models, plot
t
0
in units of
h

1
Gyr versus the matter density parameter Ω
0
,m
, for
0
≤
Ω
0
,m
≤
2
.
5. What is the general trend of
t
0
as the matter density increases?
(b) On the same plot, add a curve for
t
0
vs. Ω
0
,m
for ±at models (i.e. Ω
0
,m
+ Ω
0
,
Λ
= 1).
(c) Consider the ±at models in (b). Plot
H
0
, in units of km s

1
Mpc

1
, versus Ω
0
,m
(same range as
(b)), for 3 values of
t
0
: 11.5, 13.7, 18 Gyr. Current observations ²nd
H
0
≈
72 km s

1
Mpc

1
, and
the oldest objects in the universe is
at least
11.5 Gyr old. Given these, what is the constraint on Ω
0
,m
implied by your curves?
For some years, Ω
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This note was uploaded on 08/01/2008 for the course ASTRO 228 taught by Professor Chungpeima during the Fall '06 term at University of California, Berkeley.
 Fall '06
 CHUNGPEIMA
 Cosmology, Particle Physics

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