Chiral Photons from Chiral Gravitational Waves

We show that a parity-breaking uniform (averaged over all directions on the sky) circular polarization of amplitude $V_{00}\simeq 2.6\times {10}^{-17}\mathrm{\Delta }\chi (r/0.06)$ can be induced by a chiral gravitational-wave (GW) background with a tensor-to-scalar ratio $r$ and chirality parameter $\mathrm{\Delta }\chi$ (which is $\pm 1$ for a maximally chiral background). We also show, however, that a uniform circular polarization can arise from a realization of a nonchiral GW background that spontaneously breaks parity. The magnitude of this polarization is drawn from a distribution of root variance $\sqrt{⟨V_{00}^2⟩}\simeq 1.5\times {10}^{-18}(r/0.06{)}^{1/2}$, implying that the chirality parameter must be $\mathrm{\Delta }\chi \gtrsim 0.12(r/0.06{)}^{-1/2}$ to establish that the GW background is chiral. Although these values are too small to be detected by any experiment in the foreseeable future, the calculation is a proof of principle that cosmological parity breaking in the form of a chiral gravitational-wave background can be imprinted in the chirality of the photons in the cosmic microwave background. It also illustrates how a seemingly parity-breaking cosmological signal can arise from parity-conserving physics.