Analysis of the propagation of gravitational radiation under a graviton of nonzero mass: Cosmological constraints without electromagnetic counterparts

Under the assumptions of general relativity (GR), gravitational waves (GWs) propagate at the speed of light and their mediation can be represented as a particle through a massless graviton. We investigate the impact and observability of the presence of a massive graviton, how such a modification to GR would also modify the propagation of observed GWs from astrophysical sources, and how this effect can be used as an independent measurement of cosmological parameters. We demonstrate that a massive graviton allows the extraction of redshift information from the GWs signal, and propose a method to constrain cosmology, focusing on the Hubble parameter ${H}_{0}$ and matter energy ${\mathrm{\ensuremath{\Omega}}}_{m}$, with only GWs observations. We simulate the impact of a massive graviton on compact binary coalescence observations in a near-future Laser Interferometer Gravitational Wave Observatory-Virgo-Kamioka Gravitational Wave Detector interferometer network through a modification to the gravitational wave phase in the post-Newtonian framework. Our analysis finds that if we assume the presence of a graviton with a Compton wavelength of ${\ensuremath{\lambda}}_{G}\ensuremath{\approx}5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{m}$, corresponding to a mass ${m}_{G}\ensuremath{\le}2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{eV}/{\mathrm{c}}^{2}$, we can utilize a simulated population of 60 binary black hole observations to constrain ${H}_{0}$ to a similar precision as current gravitational wave constraints without electromagnetic counterparts (at 90% credible intervals): ${H}_{0}=5{8}_{\ensuremath{-}19}^{+34}\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ and ${\mathrm{\ensuremath{\Omega}}}_{m}=0.2{9}_{\ensuremath{-}0.08}^{+0.10}$. More sensitive observatories will be necessary to probe lower values in the graviton mass range and fully exploit this method.