A Gauge-Invariant graviton mass in Very Special Linear Gravity

Linearized gravity in the Very Special Relativity (VSR) framework is
considered. A non-zero graviton mass $m_g$ without breaking gauge
invariance nor modifying the relativistic dispersion relation is allowed. Moreover, we  explicitly show that  the massive graviton has only two physical degrees of freedom. Finally we compare some results for classical gravitational waves (GW) with the VSR ones, using the geodesic deviation equation: we find 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 $10^{-20}$. 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.