Probing Gravitational Wave Speed and Dispersion with LISA Observations of Supermassive Black Hole Binary Populations

Abstract

According to General Relativity (GR), gravitational waves (GWs) should travel at the speed of light $c$. However, some theories beyond GR predict deviations of the velocity of GWs $c_{\mathrm{gw}}$ from $c$, and some of those expect vacuum dispersion. Therefore, probing the propagation effects of GWs by comparing the wave format detectors against the one at emission excepted from GR. Since such propagation effects accumulate through larger distance, it is expected that super-massive black holes binary (SMBHB) mergers serve as better targets than their stellarmass equivalent. In this paper, we study with simulations on how observations on a population of SMBHs can help to study this topic. We simulate LISA observations on three possible SMBHB merger populations, namely Pop\MakeUppercase{\romannumeral 3}, Q3-nod and Q3-d over a 5-year mission. The resulting constraints on the graviton mass are \(9.50\), \(9.33\), and \(9.05 \times 10^{-27} \, \mathrm{eV}/c^2\), respectively. We also obtain the corresponding constraints on the dispersion coefficients assuming different dispersion scenarios. If the electromagnetic wave counterparts of SMBHB merger can be detected simultaneously, the $c_{\mathrm{gw}}$ can be constrained waveform-independently to \(Δc/c\) to \(10^{-13}-10^{-12}\), corresponding to graviton mass constraints of \(10^{-26}-10^{-24} \mathrm{eV}/c^2\).

34 pages, 9 figures, accepted for publication in Physical Review D