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We consider the possible detection of parity violation at the linear level ingravity using polarized anisotropies of the cosmic microwave background. Sincesuch a parity violation would lead to non-zero TB and EB correlations, thismakes those odd-parity angular power spectra a potential probe of parityviolation in the gravitational sector. These spectra are modeled incorporatingthe impact of lensing and we explore their possible detection in the context ofsmall-scale (balloon-borne or ground-based) experiments and a future satellitemission dedicated to B-mode detection. We assess the statistical uncertaintieson their reconstruction using mode-counting and a (more realistic) purepseudospectrum estimator approach. Those uncertainties are then translated intoconstraints on the level of parity asymmetry. We found that detecting chiralgravity is impossible for ongoing small-scale experiments. However, for asatellite-like mission, a parity asymmetry of at least 50% could be detected at68% of confidence level, and a parity asymmetry of 100% is measurable with atleast a confidence level of 95%. We also assess the impact of a possiblemiscalibration of the orientation of the polarized detectors, leading tospurious TB and EB cross-correlations. We show that in the context ofpseudospectrum estimation of the angular power spectra, self-calibration ofthis angle could significantly reduce the statistical significance of themeasured level of parity asymmetry (by e.g. a factor ~2.4 for a miscalibrationangle of 1 degree). For chiral gravity and assuming a satellite missiondedicated to primordial B-mode, a non detection of the TB and EB correlationwould translate into an upper bound on parity violation of 39% at 95%confidence level for a tensor-to-scalar ratio of 0.2, excluding values of the(imaginary) Barbero-Immirzi parameter comprised between 0.2 and 4.9 at 95% CL.

Detecting chiral gravity with the pure pseudospectrum reconstruction of the cosmic microwave background polarized anisotropies