The Graviton Mass in Very Special Relativity

Linearized gravity in the Very Special Relativity is considered. A graviton mass m_g ≠ 0 maintaining gauge invariance and the usual relativistic dispersion relation is allowed. We show that this graviton has only two physical degrees of freedom, and we compare some results for classical gravitational waves with those in Very Special Relativity using the geodesic-deviation equation. We find that the ratios between Very Special Relativity effects and classical ones are proportional to (m_g/E)² with E the graviton energy. For waves detectable by the interferometers LIGO and VIRGO, this ratio is at most 10⁻²⁰. For waves with lower frequencies in the range of future detectors, like LISA, the ratio increases significantly to 10⁻¹⁰. This combined with the anisotropic nature of Very Special Relativity phenomena may lead to observable effects.