Paper
Ringdown bounds and spectral density limits from GWTC-3
Authors
Christian Balfagon
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.16026v1</id>\n <title>Ringdown bounds and spectral density limits from GWTC-3</title>\n <updated>2026-03-17T00:20:16Z</updated>\n <link href='https://arxiv.org/abs/2603.16026v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.16026v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='gr-qc'/>\n <published>2026-03-17T00:20:16Z</published>\n <arxiv:comment>7 pages, 5 figures</arxiv:comment>\n <arxiv:primary_category term='gr-qc'/>\n <author>\n <name>Christian Balfagon</name>\n </author>\n </entry>"
}