Gravitational radiation from binary systems in Unimodular gravity

TL;DR

This paper investigates how Unimodular gravity, which allows for energy-momentum non-conservation, affects gravitational radiation from binary systems, providing new constraints on the theory using pulsar data.

Contribution

It derives modified gravitational wave emission formulas in Unimodular gravity accounting for energy non-conservation and constrains the theory parameter using pulsar observations.

Findings

Modified dispersion relation due to non-conservation

Expression for energy loss in binaries including UG effects

Stronger constraint on non-conservation parameter from pulsar data

Abstract

Unimodular gravity (UG) is classically considered identical to General Relativity (GR). However, due to restricted diffeomorphism symmetry, the Bianchi identites do not lead to the conservation of energy-momentum tensor. Thus, the conservation of energy-momentum tensor needs to be separately assumed in order to reconcile with GR. Relaxing this assumption, one finds that the conservation violation can lead to differences with GR, which can be subsequently examined in astrophysical and cosmological scenarios. To this end, we examine the predictions of UG in the context of binary systems emitting gravitational radiation. Primarily, we show how the field equations involve a diffusion function which quantifies the measure of non-conservation. Due to this violation, the dispersion relation is modified. Incorporating these changes, we provide an expression for the energy loss by the binaries, which reduces to Peters-Mathews result in the GR limit. Using binary pulsar data, we constrain the theory parameter $\zeta$ (which signifies non-conservation) by determining the rate of orbital decay. The strongest constrain on $\zeta$ comes out to be $\vert \zeta \vert \leq 5\times 10^{-4}$ which is better by an order of magnitude than an existing equivalent constraint coming from the tidal deformability of the neutron stars.