  In this thesis we focus on studying the physics of cosmological recombination
and how the details of recombination affect the Cosmic Microwave Background
(CMB) anisotropies. We present a detailed calculation of the spectral line
distortions on the CMB spectrum arising from the Lyman-alpha and the lowest
two-photon transitions in the recombination of hydrogen (H), and the
corresponding lines from helium (He). The peak of these distortions mainly
comes from the Lyman-alpha transition and occurs at about 170 microns, which is
the Wien part of the CMB. The major theoretical limitation for extracting
cosmological parameters from the CMB sky lies in the precision with which we
can calculate the cosmological recombination process. With this motivation, we
perform a multi-level calculation of the recombination of H and He with the
addition of the spin-forbidden transition for neutral helium (He I), plus the
higher order two-photon transitions for H and among singlet states of He I. We
find that the inclusion of the spin-forbidden transition results in more than a
percent change in the ionization fraction, while the other transitions give
much smaller effects. Last we modify RECFAST by introducing one more parameter
to reproduce recent numerical results for the speed-up of helium recombination.
Together with the existing hydrogen `fudge factor', we vary these two
parameters to account for the remaining dominant uncertainties in cosmological
recombination. By using a Markov Chain Monte Carlo method with Planck forecast
data, we find that we need to determine the parameters to better than 10% for
He I and 1% for H, in order to obtain negligible effects on the cosmological
parameters.
