Testing Screened Modified Gravity with Strongly Lensed Gravitational Waves

TL;DR

This paper explores how strongly lensed gravitational waves can be used to test screened modified gravity theories, developing new theoretical and statistical methods to measure deviations from General Relativity on cosmological scales.

Contribution

It introduces a refined framework for analyzing lensed GWs to constrain the post-Newtonian parameter in screened modified gravity models, addressing key degeneracies and modeling challenges.

Findings

Next-generation GW detectors can tightly constrain the PPN parameter.

Strong lensing of GWs can reveal deviations from GR on large scales.

The methods improve the measurement of time delays and magnifications in lensed GW systems.

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.