Possible consistent model of parity violations in the symmetric teleparallel gravity

TL;DR

This paper explores a symmetric teleparallel gravity model with parity violating interactions, identifying conditions under which the model remains ghost-free, thus addressing stability issues in parity violating gravity theories.

Contribution

It introduces a new parity violating symmetric teleparallel gravity model and finds specific conditions to avoid ghost instabilities in cosmological perturbations.

Findings

Most models suffer from ghost modes in vector perturbations.

A special parameter condition can eliminate ghost modes.

The model provides a stable parity violating gravity framework under certain conditions.

Abstract

Many parity violating gravity models suffer from the ghost instability problem. In this paper, we consider a symmetric teleparallel gravity model that extends the general relativity equivalent model by several parity violating interactions between the gravitational field and a scalar field. These interactions exclude higher derivatives and are quadratic in the nonmetricity tensor. Through investigations on the linear cosmological perturbations, our results show that, in general, this model suffers from the difficulty caused by the existence of ghost mode in the vector perturbations. However, in cases where a special condition is imposed on the coefficients of these parity violating interactions, this model can be ghost free.