Very Special Linear Gravity: A Gauge-Invariant Graviton Mass

TL;DR

This paper explores a gauge-invariant theory of linearized gravity within the VSR framework, allowing a non-zero graviton mass and predicting potential observable effects in future gravitational wave detectors.

Contribution

It demonstrates that graviton mass can be incorporated without gauge symmetry breaking in VSR, providing analytic solutions and analyzing potential observational signatures.

Findings

Graviton mass does not break gauge invariance in VSR.

VSR effects on gravitational waves are proportional to $(m_g/E)^2$.

Future detectors like LISA could observe VSR-induced anisotropic effects.

Abstract

Linearized gravity in the Very Special Relativity (VSR) framework is considered. We prove that this theory allows for a non-zero graviton mass $m_g$ without breaking gauge invariance nor modifying the relativistic dispersion relation. We find the analytic solution for the new equations of motion in our gauge choice, verifying as expected the existence of only two physical degrees of freedom. Finally, through the geodesic deviation equation, we confront some results for classic gravitational waves (GW) with the VSR ones: we see that the ratios between VSR effects and classical ones are proportional to $(m_g/E)^2$, $E$ being the energy of a graviton in the GW. For GW detectable by the interferometers LIGO and VIRGO this ratio is at most $10^{-20}$. However, for GW in the lower frequency range of future detectors, like LISA, the ratio increases significantly to $ 10^{-10}$, that combined with the anisotropic nature of VSR phenomena may lead to observable effects.