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Recently it was shown that the quantum vacuum effects of massless chiralfermion field in curved space-time leads to the parity-violating Pontryagindensity term, which appears in the trace anomaly with imaginary coefficient. Inthe present work the anomaly-induced effective action with the parity-violatingterm is derived. The result is similar to the Chern-Simons modified generalrelativity, which was extensively studied in the last decade, but with thekinetic terms for the scalar different from those considered previously in theliterature. The parity-breaking term makes no effect on the zero-ordercosmology, but it is expected to be relevant in the black hole solutions and inthe cosmological perturbations, especially gravitational waves.

Anomaly-induced effective action and Chern-Simons modification of general relativity