  We investigate the observational signatures of three models of the early
Universe in the $B$-mode polarization of the Cosmic Microwave Background (CMB)
radiation. In addition to the standard single field inflationary model, we also
consider the constraints obtainable on the loop quantum cosmology model (from
Loop Quantum Gravity) and on cosmic strings, expected to be copiously produced
during the latter stages of Brane inflation. We first examine the observational
features of the three models, and then use current $B$-mode polarization data
from the BICEP and QUaD experiments to constrain their parameters. We also
examine the detectability of the primordial $B$-mode signal predicted by these
models and forecast the parameter constraints achievable with future CMB
polarization experiments. We find that: (a) these three models of the early
Universe predict different features in the CMB B-mode polarization power
spectrum, which are potentially distinguishable from the CMB experiments; (b)
since $B$-mode polarization measurements are mostly unaffected by parameter
degeneracies, they provide the cleanest probe of these early Universe models;
(c) using the BICEP and QUaD data we obtain the following parameter
constraints: $r=0.02^{+0.31}_{-0.26}$ ($1\sigma$ for the tensor-to-scalar ratio
in the single field inflationary model); $m < 1.36\times 10^{-8}
\text{M}_{\text{pl}}$ and $k_{*} < 2.43 \times 10^{-4} \text{Mpc}^{-1}$
($1\sigma$ for the mass and scale parameters in the loop quantum cosmology
model); and $G\mu < 5.77 \times 10^{-7}$ ($1\sigma$ for the cosmic string
tension); (d) future CMB observations (both satellite missions and forthcoming
sub-orbital experiments) will provide much more rigorous tests of these early
Universe models.
