The Kalb-Ramond field and Gravitational Parity Violation

TL;DR

This work analyzes a parity-violating, dimension-four coupling between the Kalb-Ramond 2-form and the dual Riemann tensor, focusing on its influence on gravitational waves in an FLRW background. By deriving the GW equations of motion and mapping them to the Jenks (2023) parity-violating parameterization, the authors show that the KR interaction induces mainly phase birefringence between left and right circular polarizations, with the leading-order dispersion encoded in γ_0 ≈ -ξ(v/m_p)^2 and no significant amplitude birefringence. Using the coincident GW170817 GRB signal, they translate the speed constraint of gravitational waves into a bound on the KR background, obtaining v/m_p ≲ 4.4×10^5 (f/Hz)^{1/2} (1+z)^{-1/2}, illustrating how low-frequency, high-redshift GW observations provide the strongest tests. The results connect parity-violating gravity with KR dark-matter scenarios and motivate future multi-messenger and next-generation GW/CMB probes to explore non-minimal curvature couplings and potential Lorentz-violating effects in the gravitational sector.

Abstract

Gravitational wave physics can probe theories that extend beyond General Relativity. Motivated by the attention on the Kalb-Ramond field as a dark matter candidate, in this work, we study a parity violating dimension four operator which couples the dual Riemann curvature to the 2-form field. After mapping the equations of motion for the right- and left-handed gravitational wave amplitudes to the novel parameterization presented in \cite{Jenks:2023pmk}, we discuss constraints on the model parameters in light of the coincident electromagnetic/gravitational wave signal of GW170817.