Testing general relativity with gravitational waves -- improving and extending Modified Dispersion Relation tests

TL;DR

This paper strengthens a theory-agnostic test of general relativity by refining the modified dispersion relation (MDR) approach to gravitational-wave propagation. It replaces particle-velocity phase corrections with group-velocity corrections, expands the α-parameter space to negative values, includes higher-order modes, and adopts a Bilby-based, $A_{ m eff}$-driven sampling scheme, achieving more precise per-event posteriors and tighter bounds. The study reports an average ~19% shrinkage in posterior widths and tightens the 90% graviton-mass bound to $m_g^{90\%}<2.21\times10^{-11}$ peV/$c^2$, while finding no evidence for GR violations for negative α values. When combining 43 GWTC-3 events, the MDR bounds improve modestly compared to GWTC-3, indicating robustness of previous conclusions and providing a solid baseline for the forthcoming GWTC-4 catalog. The methodology lays groundwork for future constraints, including population-informed inferences, and highlights how negative α scenarios linked to dark-energy physics can be probed with current and upcoming GW data.

Abstract

Searching for a modified dispersion relation is one of the general relativity tests performed by the LIGO-Virgo-KAGRA collaboration with each new cumulative Gravitational Wave Transient Catalog (GWTC). It considers classes of theories that modify the dispersion of gravitational waves by introducing a massive graviton or breaking Lorentz invariance. The symmetry breaking is parameterized phenomenologically by a momentum power law term $p^α$ added to the dispersion relation, with the test placing constraints on the amplitude $A_α$ of the introduced deviation. In this work, we implement improvements to the test, chief among them group velocity parametrization, a better sampling procedure, and extension to negative exponents $α$ of $p$. We then reanalyze the events from the third catalog, GWTC-3, with our improved method. Compared with GWTC-3 results, we find significant improvement, mostly from the improved sampling method, in the posteriors obtained by analyzing individual event and more modest improvements in the combined bounds on amplitude parameters $A_α$ -- on average, we observe 19% shrinking of posterior width. The 90% upper bound on the graviton mass changes from $2.42 \times 10^{-11}$ peV to $2.21 \times 10^{-11}$ peV. For the extension of our test to $α\in \{-1, -2, -3\}$, we find no evidence in favor of general relativity violation.

Figures (14)

• Figure 1: Posterior on the the MDR phase correction $\delta\Psi$ for a GW190412_053044-like injection (GR). The HM content in the signal produces constraints on the possible values of $\delta\Psi$, in contrast to the uniform posterior expected from a signal with no HM content.
• Figure 2: The posterior of the $A_1$ amplitude parameter for a GW190412_053044-like injection. Top: Multiple values of $A_1$ correspond to the same correction to the waveform phase $\delta\Psi$, splitting the posterior between different branches. Bottom: On a large scale, this results in a uniform $A_1$ posterior.
• Figure 3: Example frequency-dependence of the speed of GWs $c_{\rm gw}$, where approximate LVK and LISA bands are highlighted. The behavior shown here is representative of what can be encountered in theories of dark energy that affect $c_{\rm gw}$ on cosmological scales, with an asymptotic low-frequency speed $c_{\rm gw} = c_{\rm gw}(0)$ and a transition to $c_{\rm gw} = c$ as one approaches the LVK band. The high-frequency tail of this transition is what the MDR analyses in the LVK band test and this corresponds to probing negative values of $\alpha$ in \ref{['mdr_speed']}. See the main text for further details.
• Figure 4: The pp-plot for the injection test of MDR. For clarity, we plotted just the sampled non-GR parameter ($A_{\mathrm{eff}}$, $m_{\mathrm{eff}}$ or $\delta\Psi_{MDR}$, depending on the injection set). The p-values were computed from KS statistics, and are consistent with a uniform distribution of percentiles. The combined p-value across the non-GR parameters is 0.49.
• Figure 5: The GW190412_053044 posteriors for $\alpha=0$ (left) and $\alpha=3.5$ (right) dispersions. Three posteriors are plotted: one obtained using the IMRPhenomXPHM waveform (blue), one using the IMRPhenomXP waveform (orange), and one from the GWTC-3 MDR analysis (green), also using the IMRPhenomXP waveform. Dashed vertical lines indicate the median and the 90% CI. For $\alpha=0$, we see a drastic reduction in the width of the posterior, while the width stays similar for the $\alpha=3.5$ case. These are illustrative for other analyses of events with significant HM content.