Ringdown bounds and spectral density limits from GWTC-3

TL;DR

This paper uses gravitational wave data to set bounds on nonlocal gravity theories, constraining their spectral density parameters and providing benchmarks for future tests across multiple physics domains.

Contribution

It presents the first observational bounds on nonlocal gravity extensions using GW data and maps these bounds onto the spectral parameter space, excluding certain infrared-extended spectral densities.

Findings

Set an upper limit on quasi-normal mode deformations |epsilon_Omega| < 0.05

Excluded broad classes of spectral densities with mu <= 10^{-6} m^{-2}

Identified sub-millimetre gravity experiments as promising for direct tests

Abstract

We establish the first observational bounds on causal nonlocal extensions of gravity characterized by retarded Stieltjes-type kernels with positive spectral density rho(mu) >= 0, using two complementary gravitational-wave channels. From a Bayesian ringdown analysis of 17 binary black hole events in the LIGO-Virgo GWTC-3 catalogue, we set an observational ceiling on universal fractional quasi-normal mode deformations of |epsilon_Omega| < 0.05 (90% C.L.), with a cumulative log Bayes factor ln B = -0.46 +/- 0.77. By mapping published GWTC-3 modified dispersion relation bounds together with the GW170817 propagation speed constraint onto the Stieltjes spectral parameter space (mu_char, M0), we exclude a broad class of infrared-extended spectral densities with mu <= 10^{-6} m^{-2}, thereby ruling out non-trivial regions of the nonlocal kernel parameter space for the first time. The theoretically motivated fiducial range mu_char ~ M_*^2 ~ 10^8-10^10 m^{-2} satisfies all current bounds. We further show that sub-millimetre gravity experiments, which already operate at the predicted causal scale l_* ~ 10^{-4} m, provide the most promising path toward a direct test. These results define quantitative benchmarks against which future observations across the gravitational-wave, short-range gravity, and cosmological sectors can be compared.