COSMOLOGY
Problem Set 9
May 24, 2010
Problem 1: Variations on SBBN
a) Some recent experiments suggest that the neutron lifetime may be smaller than
the currently accepted value. Suppose this were true and describe, qualitatively, the
eect this would have
COSMOLOGY
Problem Set 8
May 19, 2010
Problem 1: Dark Matter Candidate
Consider a spin 1/2, symmetric ( = 0), massive fermion whose annihilation rate
factor is mass-dependent: = v = 5.01021/m2 (GeV) cm3 /s. For m = 300 GeV,
nd:
a) T (and x ). [Hint: You wi
COSMOLOGY
Problem Set 7
May 10, 2010
Problem 1: Another Sterile Neutrino
Suppose there is a new, very weakly interacting, sterile neutrino s which does
not mix with the usual (active) neutrinos. The s are light but not massless
(0 = ms 1 MeV).
a) If these
COSMOLOGY
Problem Set 6
May 3, 2010
Problem 1: Bosonic Neutrinos
Suppose the three standard neutrinos (e , , ) were Bosons instead of Fermions.
For temperatures in the range me T m , nd:
a) The new eective number of degrees of freedom gef f . [5]
b) The e
COSMOLOGY
Problem Set 5
April 26, 2010
Problem 1: CDM
Consider the standard CDM cosmological model with M = 0.25 and = 0.75;
you may adopt H0 = 70 kms1 Mpc1 . Assume that the current density in relativistic
particles (radiation) is R = 8.0 105 .
a) Find t
COSMOLOGY
Problem Set 4
April 19, 2010
Problem 1 : k-Matter
Assume that the Universe is at (k = 0) and that the energy density is dominated
by a eld (X ) whose equation of state is: wX = 1/3.
a) For this model nd X as a function of the scale factor (or, o
COSMOLOGY
Problem Set 3
April 12, 2010
Problem 1 : Matter Dominated Evolution
Consider a Matter Dominated (MD: p = 0, = 0) Robertson-Walker-Friedman
cosmological model.
a) Find the density parameter as a function of the redshift, (z ), and its present
val
COSMOLOGY
Problem Set 2
April 7, 2010
Problem 1 : Collapse of a Uniform Sphere
This is really a problem in Newtonian mechanics. Consider a uniform (homogeneous) sphere of mass M whose initial radius (at t = 0) is R0 . The sphere is released
from rest at t
COSMOLOGY
Problem Set 1
March 31, 2010
Problem 1 : Local Universe
In the limit of small distances, geometry is Euclidean (locally at). For a at cosmology, r = , R = R, A = 4R2 , and V = 4R3 /3. For k = 0 (k = 1), nd the
leading order corrections to the fo