This paper tests whether a simple, physically motivated modification of gravity can explain both cosmological data and the way gravitational waves stretch as they travel. The authors study a scalar field that is non‑minimally coupled to gravity. That coupling makes the effective strength of gravity change over time. On cosmological scales this change shows up as a nonzero “Planck mass running rate,” usually written α_M(z). That same effect damps gravitational waves as they travel and so changes the distance to a source inferred from gravitational waves relative to the distance inferred from light (electromagnetic) signals.

The researchers start from a particular non‑minimally coupled (NMC) scalar‑tensor model that previous work showed can fit measurements of the universe’s expansion, including recent galaxy surveys (DESI), the cosmic microwave background (Planck and ACT), and supernova data. They use that model to predict the function α_M(z) and the resulting ratio of gravitational‑wave to electromagnetic luminosity distances, D_L^GW/D_L^EM. They then translate those predictions into two commonly used, simpler parameter forms: one called c_M, which assumes α_M scales like the fractional dark energy density, and a distance model parametrized by (Ξ_0, n) that directly modifies the GW/EM distance ratio.

When mapped onto these simple forms the NMC model predicts c_M = −0.5 ± 0.2 and Ξ_0 = 0.88 ± 0.05 with n = 3.2 ± 0.3. Those numbers are consistent with the current constraints from the LIGO‑Virgo‑KAGRA catalog (GWTC‑5) at about the one‑sigma level or better. The authors emphasize that this agreement is largely driven by the large uncertainties that remain in current gravitational‑wave measurements. With present data those measurements allow both the standard cosmological model (ΛCDM) and the NMC model.