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 .