Very Special Linear Gravity: A Gauge-Invariant Graviton Mass

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.

Latex,6 pages

References in corpus (3)

• Resummation of Massive Gravity
• Very Special Relativity
• New Graviton Mass Bound from Binary Pulsars

Cited by in corpus (7)

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• Renormalization of Very Special Relativity gauge theories
• Graviton Mass Bounds in Very Special Relativity from Binary Pulsar's Gravitational Waves
• Corrections to the Gyromagnetic Factor in Very Special Relativity
• VSL-Gravity in light of PSR B1913+16 Full Data Set: Upper limits on graviton mass and its theoretical consequences
• Vacuum polarization and induced Maxwell and Kalb-Ramond effective action in very special relativity
• Generalized Mandelstam-Leibbrandt regularization