Ghost-free 2-form fields in cosmology: implications for gravitational parity violation

TL;DR

This paper investigates ghost-free, parity-violating 2-form field theories in cosmology, demonstrating that parity violation can lead to chiral gravitational waves, with implications for gravitational parity violation models.

Contribution

It introduces a family of ghost-free, parity-violating 2-form theories and analyzes their cosmological tensor perturbations, revealing conditions for chiral gravitational wave generation.

Findings

Parity-violating terms can be absorbed into a field redefinition.

Chiral gravitational waves can be generated with parity-violating potential terms.

The theory remains ghost-free and dynamically consistent.

Abstract

We explore the possibility of parity-violating, nonminimally coupled 2-form field theories that retain the same dynamical degrees of freedom as a massive 2-form and thus are ghost-free. Starting from the most general kinetic terms and dimension four couplings between the 2-form field and the curvature tensors, we find a two-parameter family of such theories. However, we also find that parity-violating terms involving the dual 2-form field can be absorbed into a field redefinition, leaving a theory with essentially the same structure as that obtained by Heisenberg and Trenkler (i.e., the parity-preserving coupling to the double dual Riemann tensor). After the field redefinition, the only place where parity-violating terms can appear is in the potential. We then consider a homogeneous and isotropic cosmological model with an isotropic configuration of a triplet of 2-form fields, and study tensor perturbations in this setup. There are three types of tensor perturbations, two of which are dynamical. We show that chiral gravitational waves can be generated in the presence of parity-violating terms in the potential.