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

TL;DR

The paper investigates how LISA observations of SMBHB populations can constrain GW dispersion and speed beyond GR by modeling dispersion as $E^2 = p^2 + \mathbb{A}_\alpha p^\alpha$ with $\mathbb{A}_0 = m_g^2$, and by analyzing three SMBHB population realizations with Bayesian inference on $\mathbb{A}_\alpha$ for various discrete $\alpha$. It shows that individual high-SNR SMBHBs can constrain $m_g$ to about $10^{-26}$ eV/$c^2$, with stronger bounds tied to higher chirp mass and SNR; joint analyses across populations improve these limits and reveal how constraints scale with source properties. The study also demonstrates that with electromagnetic counterparts, joint LISA–X-ray observations can bound the GW speed deviation $\Delta c/c$ to the $10^{-13}-10^{-12}$ range, translating to graviton masses of $10^{-26}-10^{-24}$ eV/$c^2$, depending on detector sensitivity. Overall, SMBHB populations observed by LISA offer significantly stronger and more robust tests of GW dispersion than current ground-based detectors, and multi-messenger observations further strengthen these constraints.

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 $c_{\rm gw}$ 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 $c_{\rm gw}$ can be constrained waveform-independently to \(Δc/c\) to \(10^{-13}-10^{-12}\), corresponding to graviton mass constraints of \(10^{-26}-10^{-24} \mathrm{eV}/c^2\).

Figures (10)

• Figure 1: A comparison of the waveforms received by LISA with and without the graviton mass: The horizontal axis represents time, assuming the burst occurs at $10^6$ s. The vertical axis represents the response detected by one of LISA's interferometers. The graviton mass is assumed to be $m_g = 10^{-24} \mathrm{eV}/c^2$, with other source parameters given in Table \ref{['value1570']}.
• Figure 2: The distributions of chirp mass and luminosity distance (upper panel) or SNR (lower panel) for the sources in the three catalogs.
• Figure 3: The plot shows the upper limits on the graviton mass constrained using two different methods: The blue dashed line represents the reference line where the two values are equal. The horizontal axis corresponds to the upper limit on the graviton mass constrained using non-dispersive waveforms, i.e., Non-dispersion mass (NDM), and the vertical axis corresponds to the upper limit on the graviton mass that can be detected, i.e., minimum detectable mass (MDM).
• Figure 4: Corner figure of the posterior distributions for the parameters of the example source: The parameters are in order: total mass $m_{\rm T}$ in unit of $M_\odot$, mass ratio $q\equiv m_2/m_1$, dimensionless spin $\chi_1$ of the primary BH, dimensionless spin of $\chi_2$ of the secondary BH, luminosity distance $d_{\rm L}$ in unit of Mpc, the reference time $t_{\rm ref}$ corresponding to the frequency at which the signal’s energy output is maximal in unit of s and the square of the graviton mass $m^2_g$ in unit of ($\mathrm{eV}/c^2)^2$.
• Figure 5: The distributions of the upper limit on the graviton mass and SNR (upper panel), chirp mass (middle panel) or luminosity distance (lower panel) for the sources in the three catalogs.