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 thus come to the subject of BBN: the production of t
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 2 109 ; T me ).
Big Bang nucleosynthesis (z 2 108 ).
No
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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 intrinsic luminosity, 15% after applying corrections.
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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 energy as seen by an observer with 4-velocity u is
E = u P
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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 are not special. Copernicus
Mathematically easiest to an
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 (, )
=
B
Ylm ab (, )
=
2
(l 1)l(l + 1)(l + 2)
1
(
(l 1)
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 not use the properties of the spherical Bessel functio
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, and on superhorizon scales k/aH
1, the density and pote
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 < 1/3.
(a) Calculate the relation between and aH in th
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
massless particle varies as:
p = aH + pi
A
Bi
+ pi pj j + D
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
2 nH,tot
x2
eLy /T
4x1
.
(1)
This problem presents an
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 addition to e , , and . (This possibility is now excluded
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
=5500 (green) and has a width = 900. The magnitude V in t
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 metric, for general f ().
(b) Compute the Ricci tensor