Very special linear gravity: A gauge-invariant graviton mass

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