Polarized primordial gravitational waves in the ghost-free parity-violating gravity

TL;DR

This paper investigates the polarization of primordial gravitational waves in a ghost-free parity-violating gravity theory, finding that higher derivatives influence polarization similarly to Chern-Simons gravity, but detection remains challenging.

Contribution

It provides an analytical study of PGW polarization in a generalized ghost-free parity-violating gravity, including higher derivatives, and compares their effects to Chern-Simons gravity.

Findings

Higher derivatives contribute similarly to Chern-Simons gravity in polarization.

Degree of polarization is suppressed by the parity violation energy scale.

Detection via two-point statistics from CMB data is unlikely.

Abstract

The tests of parity symmetry in the gravitational interaction is an attractive issue in the gravitational-wave astronomy. In the general theories of gravity with parity violation, one of the fundamental results is that the primordial gravitational waves (PGWs) produced during the slow-roll inflation is circularly polarized. In this article, we investigate the polarization of PGWs in the recently proposed ghost-free parity-violating gravity, which generalizes the Chern-Simons gravity by including the higher derivatives of the coupling scalar field. For this purpose, we first construct the approximate analytical solution to the mode function of the PGWs during the slow-roll inflation by using the uniform asymptotic approximation. With the approximate solution, we calculate explicitly the power spectrum and the corresponding circular polarization of the PGWs analytically, and find that the contributions of the higher derivatives of the coupling scalar field to the circular polarization is of the same order of magnitude as that of Chern-Simons gravity. The degree of circular polarization of PGWs is suppressed by the energy scale of parity violation in gravity, which is hardly detected on the basis solely of two-point statistics from future cosmic microwave background data.