The detection of gravitational waves (GWs) has opened a new window to test the fundamental nature of gravity. We present constraints on the nonstandard propagation of GWs using the spectral siren method applied to binary black hole (BBH) mergers from the third Gravitational-Wave Transient Catalog (GWTC-3). The spectral siren method exploits the redshift distribution of BBHs to probe the cosmic expansion history and break degeneracies between cosmology and modified gravity effects. We focus on the friction term v in the nonstandard GW propagation equation, which characterizes the running of the Planck mass. Assuming the standard ΛCDM cosmology, we find <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\nu=-1.1_{-1.1}^{+3.9},\ \nu=0.5_{-2.6}^{+3.5}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>ν</mi> <mo>=</mo> <mo>−</mo> <msubsup> <mn>1.1</mn> <mrow> <mo>−</mo> <mn>1.1</mn> </mrow> <mrow> <mo>+</mo> <mn>3.9</mn> </mrow> </msubsup> <mo>,</mo> <mi>ν</mi> <mo>=</mo> <msubsup> <mn>0.5</mn> <mrow> <mo>−</mo> <mn>2.6</mn> </mrow> <mrow> <mo>+</mo> <mn>3.5</mn> </mrow> </msubsup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\nu=0.7_{-2.3}^{+3.1}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>ν</mi> <mo>=</mo> <msubsup> <mn>0.7</mn> <mrow> <mo>−</mo> <mn>2.3</mn> </mrow> <mrow> <mo>+</mo> <mn>3.1</mn> </mrow> </msubsup> </math></EquationSource> </InlineEquation> (median and 90% credible interval) for the Truncated, Power Law + Peak, and Broken Power Law mass models, respectively. These results improve upon previous constraints from the bright siren event GW170817 by an order of magnitude, owing to the higher redshifts of BBHs in GWTC-3, which reach up to z ∼ 1. Our result suggests that the propagation of GWs is consistent with the predictions of general relativity, placing limits on modified gravity theories that predict a time-varying Planck mass. As the sensitivity of GW detectors improves, the spectral siren method will provide a powerful tool for testing gravity on cosmological scales and probing the physics of the early Universe.

Constraining the nonstandard propagating gravitational waves in the cosmological background with GWTC-3

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发表日期：

2026年1月4日

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Zu-Cheng Chen,
Lang Liu

摘要

The detection of gravitational waves (GWs) has opened a new window to test the fundamental nature of gravity. We present constraints on the nonstandard propagation of GWs using the spectral siren method applied to binary black hole (BBH) mergers from the third Gravitational-Wave Transient Catalog (GWTC-3). The spectral siren method exploits the redshift distribution of BBHs to probe the cosmic expansion history and break degeneracies between cosmology and modified gravity effects. We focus on the friction term v in the nonstandard GW propagation equation, which characterizes the running of the Planck mass. Assuming the standard ΛCDM cosmology, we find $\nu=-1.1_{-1.1}^{+3.9},\ \nu=0.5_{-2.6}^{+3.5}$ $ν = - {1.1}_{- 1.1}^{+ 3.9}, ν = {0.5}_{- 2.6}^{+ 3.5}$ and $\nu=0.7_{-2.3}^{+3.1}$ $ν = {0.7}_{- 2.3}^{+ 3.1}$ (median and 90% credible interval) for the Truncated, Power Law + Peak, and Broken Power Law mass models, respectively. These results improve upon previous constraints from the bright siren event GW170817 by an order of magnitude, owing to the higher redshifts of BBHs in GWTC-3, which reach up to z ∼ 1. Our result suggests that the propagation of GWs is consistent with the predictions of general relativity, placing limits on modified gravity theories that predict a time-varying Planck mass. As the sensitivity of GW detectors improves, the spectral siren method will provide a powerful tool for testing gravity on cosmological scales and probing the physics of the early Universe.