Polarization states of gravitational waves with a massive graviton

TL;DR

This paper derives explicit polarization modes for massive gravitons in a specific bimetric theory, showing that extra polarization states are negligible at high frequencies but significant at very low frequencies, with implications for future gravitational wave and CMB observations.

Contribution

It provides explicit expressions for polarization modes of massive gravitons within a bimetric theory, highlighting frequency-dependent differences from general relativity.

Findings

Extra polarization states are much smaller than GR polarizations in the VIRGO-LIGO band.

At very low frequencies (~10^(-7) Hz), extra polarization states become comparable to GR states.

The results can help constrain graviton mass through future gravitational wave and CMB experiments.

Abstract

Using the Newman-Penrose formalism, we obtain the explicit expressions for the polarization modes of weak, plane gravitational waves with a massive graviton. Our analysis is restricted for a specific bimetric theory whose term of mass, for the graviton, appears as an effective extra contribution to the stress-energy tensor. We obtain for such kind of theory that the extra states of polarization have amplitude several orders of magnitude smaller than the polarizations purely general relativity (GR), h_(+) and h_(x), in the VIRGO-LIGO frequency band. This result appears using the best limit to the graviton mass inferred from solar system observations and if we consider that all the components of the metric perturbation have the same amplitude h. However, if we consider low frequency gravitational waves (e.g., f_(GW) ~ 10^(-7) Hz), the extra polarization states produce similar Newman-Penrose amplitudes that the polarization states purely GR. This particular characteristic of the bimetric theory studied here could be used, for example, to directly impose limits on the mass of the graviton from future experiments that study the cosmic microwave background (CMB).