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 fsky ∼ 0:02--0:2 could place a 2sigma r ≈ 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 ( fsky = 0:75) sky would give 2sigmar ≈ 0:015, rising to ≈ 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 Xe around the fiducial 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 Xe. We study various properties of these modes, including their convergence, fiducial model-dependence, dataset dependence, and the eigen-modes response to marginalization over different standard parameters. We demonstrate that, if enough modes are included, the eigen-modes form a practically complete set of basis function for expanding different physically motivated Xe perturbations. We also develop an information-based criterion to truncate the eigen-mode hierarchy, which can be used in similar hierarchical model selections as well. We show how our measurements of cosmic parameters will be affected if possible deviations in the recombination history are ignored. The method is applied to simulations of Planck+ACTPol and a cosmic variance limited survey with differing simulated recombination histories and the recovered Xe trajectories are constructed. We also apply the method to the best currently available CMB datasets, WMAP9+ACT/SPT. The first constructed eigen-mode turns out to be a direct measure of the damping envelope. Its current measurement with SPT slightly indicates a damping tail anomaly, while ACT data agree well with the standard scenario. High resolution Planck data will resolve this tension with high significance.
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