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

TL;DR

This paper derives an anomaly-induced effective action incorporating a parity-violating Chern-Simons term in general relativity, highlighting potential implications for black holes and gravitational waves.

Contribution

It introduces a new form of the effective action with a parity-violating term, differing from previous models, and explores its potential physical effects.

Findings

Parity-violating term does not affect zero-order cosmology

Potential relevance in black hole solutions

Impacts on cosmological perturbations and gravitational waves

Abstract

Recently it was shown that the quantum vacuum effects of massless chiral fermion field in curved space-time leads to the parity-violating Pontryagin density term, which appears in the trace anomaly with imaginary coefficient. In the present work the anomaly-induced effective action with the parity-violating term is derived. The result is similar to the Chern-Simons modified general relativity, which was extensively studied in the last decade, but with the kinetic terms for the scalar different from those considered previously in the literature. The parity-breaking term makes no effect on the zero-order cosmology, but it is expected to be relevant in the black hole solutions and in the cosmological perturbations, especially gravitational waves.