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 $\gamma_{\text{PN}}$ 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 ($\gamma_{\text{PN}}$) across different screening scales ($\Lambda$). 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.