Testing Screened Modified Gravity with Strongly Lensed Gravitational Waves

Abstract

Screening mechanisms are essential components in many modified gravity theories, which satisfy local tests of General Relativity (GR) and address cosmic acceleration on cosmological scales. The strong gravitational lensing of gravitational waves (GWs) offers a unique observational probe into cosmology and fundamental physics. In this paper, we investigate the possibility of testing screened modified gravity theories with strongly lensed gravitational waves. Specially, we develop the refined theoretical and statistical framework, in order to measure the post-Newtonian parameter $γ_{\text{PN}}$ in the presence of screening effects. Specially, the mass-truncated power-law and Navarro-Frenk-White (NFW) models are introduced to quantify the modified lensing potential. Our analysis also addresses the mass-sheet degeneracy (MSD) problem, by incorporating the absolute magnification and time delay measurements accessible through strongly lensed GW systems. We find that individual lensed GW system detected by next-generation GW detectors can provide stringent constraints on the PPN parameter ($γ_{\text{PN}}$) across different screening scales ($Λ$). Therefore, future measurements of strongly lensed GWs have great promise to seek departures from GR on kpc-Mpc scales, due to more precise time delay from lensed GW signals.

Figures (3)

• Figure 1: Posterior probability distributions of the model parameters for Event I. The diagonal panels show the 1-D marginalized distributions with dashed lines indicating the median and the $1\sigma$ confidence intervals (16% and 84%). The off-diagonal panels display the 2-D joint confidence regions.
• Figure 2: One-dimensional posterior probability distributions of the Post-Newtonian parameter $\gamma_\mathrm{PN}$. The left columns (a), (c) and right columns (b), (d) correspond to System I and System II, respectively. The top row shows the recovered results for an injected signal consistent with GR ($\gamma_\mathrm{PN}=1$), while the bottom row displays the results for a simulated modified gravity signal ($\gamma_\mathrm{PN}=1.1$). The solid blue lines indicate the fiducial values, and the vertical dashed lines represent the 68% ($1\sigma$) confidence intervals.
• Figure 3: Constraints on the post-Newtonian parameter $\gamma_\mathrm{PN}$ as a function of the screening scale $\Lambda$ (in kpc). The results are derived from an ensemble of 250 independent MCMC simulations. The solid blue line indicates the median of the posterior distributions, while the light blue shaded region represents the $1\sigma$ (68%) confidence interval. The widening of the confidence band indicates that the constraints on $\gamma_\mathrm{PN}$ degrade as the screening scale $\Lambda$ increases.