We discuss the polarization signature of primordial gravitational waves imprinted in cosmic microwave background (CMB) anisotropies. The high-energy physics motivated by superstring theory or M-theory generically yield parity violating terms, which may produce a circularly polarized gravitational wave background (GWB) during inflation. In contrast to the standard prediction of inflation with un-polarized GWB, circularly polarized GWB generates non-vanishing TB and EB-mode power spectra of CMB anisotropies. We evaluate the TB and EB-mode power spectra taking into account the secondary effects and investigate the dependence of cosmological parameters. We then discuss current constraints on the circularly polarized GWB from large angular scales (l < 16) of the three year WMAP data. Prospects for future CMB experiments are also investigated based on a Monte Carlo analysis of parameter estimation, showing that the circular polarization degree, varepsilon, which is the asymmetry of the tensor power spectra between right- and left-handed modes normalized by the total amplitude, can be measured down to |varepsilon| 0.35(r/0.05)^{-0.6}.
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