Graduate Department of Astronomy and Astrophysics, University of Toronto

In this thesis we investigate the two cosmic epochs of inflation and recombination, through their imprints on the temperature and polarization anisotropies of the cosmic microwave background radiation.

To probe the early universe we develop a map-based maximum-likelihood estimator to
measure the amplitude of inflation-induced gravity waves, parametrized by *r*, from the cosmic
microwave background (CMB) polarization maps. Being optimal by construction, the estimator
avoids *E-B* mixing, a possible source of contamination in the tiny *B*-mode detection, the target
of many current and near future CMB experiments. We explore the leakage from the *E-* to
the *B-*mode of polarization by using this estimator to study the linear response of the *B-*mode
signal at different scales to variations in the *E-*mode power. Similarly, for various observational
cases, we probe the dependence of *r* measurement on the signal from different scales of *E*
and *B* polarization. The estimator is used to make forecasts for Spider-like and Planck-like
experimental specifications and to investigate the sky-coverage optimization of the Spider-like
case. We compare the forecast errors on *r* to the results from a similar multipole-based estimator
which, by ignoring the mode-mixing, sets a lower limit on the achievable error on *r*. We find that
an experiment with Spider-like specifications with f_{sky} ~ 0.02-0.2 could place a 2 sigma_{r}
approx. 0.014 bound (~ 95% CL), which rises to 0.02 with an *l*-dependent foreground residual left over
from an assumed efficient component separation. For the Planck-like survey, a Galaxy-masked
(f_{sky} = 0.75) sky would give 2 sigma_{r} approx. 0:015, rising to approx. 0.05 with the foreground residuals. We
also use a novel information-based framework to compare how different generations of CMB
experiments reveal information about the early universe, through their measurements of *r*.

We also probe the epoch of recombination by investigating possible fluctuations in the free
electron fraction *X _{e}* around the ducial model of the standard recombination scenario. Though
theoretically well studied, the detailed assumptions in the recombination history, based on
standard atomic physics, have never been directly tested. However, for our CMB-based cosmological
inferences to be reliable, the recombination scenario needs to be observationally verified.
We approach this problem in a model-independent way and construct rank-ordered parameter
eigen-modes with the highest power to probe