Cosmology Problem Set 6
1. In class we did not work out the steps for the continuity equation and the Euler equation.
In this problem you are going to do that.
Write down the continuity equation and perturb it as we did in class. Now keep only linear
orde

Cosmology Problem Set 7
1. Using Poissons equation, show that the Harrison-Zeldovich power spectrum gives potential fluctuations, that are scale invariant.
2. a) Assume a pre-inflationary epoch, that is radiation dominated. Using the expression
of the hor

Cosmology Problem Set 2
1. Solve the acceleration equation and show that for matter and radiation only universes we
obtain a deccelerating universe. Now solve the acceleration equation using a cosmological
constant only universe and show that we get an ex

Cosmology Problem Set 3
1. In high energy Physics one uses the natural units in which ~ = c = KB = 1. Every
physical quantity is quoted in terms of energy units (ev, Mev, Gev etc). In this unit system
find the dimensions of
a) mass, length, time, temperat

Cosmology Problem Set 4
1. In class we derived the horizon distance for single component Universes.
a) Calculate the horizon scale at the surface of last scattering (z=1100) for a matter dominated Universe (approximate scenario of the Universe during reco

Cosmology Problem Set 1
1. H or the Hubble parameter has dimension of inverse time. Hence the inverse of the
Hubble parameter gives a time scale of the Universe. Using the current value of H0 = 71
ks/s/Mpc, find out the equivalent timescale. The current a