A simple parity violating model in the symmetric teleparallel gravity and its cosmological perturbations

TL;DR

This paper explores a simple parity-violating extension of symmetric teleparallel gravity, revealing novel dynamical vector modes with different propagation speeds and identifying a high-momentum ghost issue affecting quantum stability.

Contribution

It introduces a parity non-conserved coupling in symmetric teleparallel gravity and analyzes its effects on cosmological perturbations, highlighting new dynamical vector modes and stability challenges.

Findings

Vector perturbations become dynamical and propagate with different velocities.

Parity violation affects tensor and vector perturbations.

High-momentum vector mode is a ghost, indicating potential quantum instability.

Abstract

The parity violating gravity models based on the symmetric teleparallel gravity have been considered in the literature, but their applications in cosmology and especially the modifications to cosmological perturbations have not been fully explored. In this paper we consider such a simple model which modifies general relativity by a parity non-conserved coupling, within the framework of the symmetric teleparallel gravity. We study in detail its cosmological applications and focus on its cosmological perturbation theory. Besides the already known parity violation in the tensor perturbations, we find that the vector perturbations in this model are promoted to be dynamical degrees of freedom, and the left- and right-handed vector modes propagate with different velocities. More importantly, we find that one of the vector modes is a ghost at high momentum scales, which will give rise to the problem of vacuum instability in the quantum theory of cosmological perturbations.