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}≃2.6×10^{-17}Δχ(r/0.06) can be induced by a chiral gravitational-wave (GW) background with a tensor-to-scalar ratio r and chirality parameter Δχ (which is ±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}⟩]≃1.5×10^{-18}(r/0.06)^{1/2}, implying that the chirality parameter must be Δχ≳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.