Chiral gravitational effect in time-dependent backgrounds

Gravitational counterpart of the chiral magnetic effect, which is referred as the chiral gravitational effect, can also be of interest in a cosmological setup. In this study, we investigate this effect in the time-dependent chiral asymmetric fermion background and in the expanding spacetime by formulating the effective action of gravitational waves. We also analyze the anomaly equation to see how the backreaction from gravitational waves to thermal chiral plasma occurs. We find that the non-trivial time dependence of chiral chemical potential, which can be induced in some scenarios of baryogenesis, is the key ingredient of the chiral gravitational effect. It turns out that the "memory" of the effect is imprinted on the high frequency gravitational waves propagating in the plasma. Cosmological implications and potential effects on the gravitational wave observation are briefly discussed.