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 } \Delta \chi ( r / 0.06 ) can be induced by chiral gravitational-wave ( GW ) background with tensor-to-scalar ratio r and chirality parameter \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 non -chiral GW background that spontaneously breaks parity .
The magnitude of this polarization is drawn from a distribution of root-variance \sqrt { \left < { V _ { 00 } ^ { 2 } } \right > } \simeq 1.5 \times 10 ^ { -18 } ( r / 0.06 ) ^ { 1 / 2 } implying that the chirality parameter must be \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 .