1
Big Bang Nucleosynthesis: Overview
A few seconds after the Big Bang, almost all of the energy density in the Universe
was in photons, neutrinos, and e+ e pairs, but some was in the form of baryons.
We now follow the thermal history of the Universe. (c.f. Dodelson 2.4, 3.1,
3.2). The major steps here will be:
Relativistic plasma (z 1010 ).
Neutrino decoupling (z 1010 ).
e+ e annihilation (z 2
1
Type Ia Supernovae
The Type Ia supernovae (SN Ia) are the most popular standard candle in cosmology today.
Advantages:
Can be seen to cosmologically signicant distances, z 1.8.
Small dispersion in
1
Redshift and conformal time
Photon trajectories. Recall from GR that a photons trajectory is described
by x (s) where s is the ane parameter. The photons momentum is
P =
dx
.
ds
(1)
The photons ener
1
Cosmological principle
Basic assumption. The Universe on large scales is homogeneous and isotropic.
(The cosmological principle.)
Why make this assumption? Initally a philosophical principle:
We ar
Ph217c, Homework 6.
Due Thursday, May 29, 2008.
1. [50%] Properties of tensor spherical harmonics. Consider the tensor
E
B
spherical harmonics Ylm ab (, ) and Ylm ab (, ) discussed in class:
E
Ylm ab
Ph217c, Homework 5.
Due Thursday, May 15, 2008.
1. [50%] Practice with spherical Bessel functions. For this problem
you may use any of the tabulated properties of the Legendre polynomials, but
you may
Ph217c, Homework 4.
Due Thursday, May 1, 2008.
1. [35%] Superhorizon perturbations in the matter era. Use the
conservation of the curvature perturbation to prove that after matter-radiation
equality,
Ph217c, Homework 3.
Due Thursday, April 24, 2008.
1. [60%] Gravitational waves from power-law expansion. Suppose
that the Universe underwent an inationary epoch with constant w = p/ in
the range 1 < w
Ph217c, Homework 1.
Due Thursday, April 10, 2008.
1. [40%] Momentum evolution for a massless particle. In class, it was
claimed that to rst order in perturbation theory, the spatial momentum of a
mass
Ph 217b Homework 4.
DUE: Thursday, March 13, 2008.
1. [35%] Alternate derivation of Lyman- redshifting. In class we
derived the net downward transition rate from emitting Lyman- photons,
x2 =
3
HLy
Ph217b, Homework 3.
Due Thursday, March 6, 2008.
1. [40%] Neutron abundance at freeze-out. Dodelson #3.4.
2. [20%] Extra neutrinos. Suppose that there was a fourth generation of
active neutrinos in ad
Ph217b, Homework 2.
Due Thursday, February 28, 2008.
1. [20%] Practice with magnitudes. This problem deals with magnitudes
in the visual (V ) waveband. This waveband is centered at a wavelength of
=5
HOMEWORK 1 Ph217b COSMOLOGY
Due Tuesday February 19, 2008.
1. [50%] We considered in class the FRW metric,
ds2 = dt2 + a2 (t)[d2 + f ()(d2 + sin2 d2 )].
(1)
(a) Compute the Christoel symbols for this