New probe of gravity: strongly lensed gravitational wave multi-messenger approach

TL;DR

This paper introduces a multimessenger method combining gravitational wave and electromagnetic data from strongly lensed events to test and constrain modified gravity theories on galactic scales.

Contribution

It proposes a novel multimessenger approach using GW and EM data to constrain scale-dependent modified gravity parameters, improving robustness and reducing uncertainties.

Findings

GW time-delay data can detect 18% MG effects at 68% confidence

A simplified consistency relation can identify 8% MG effects without velocity dispersion data

The approach enhances understanding of gravity on galactic and extra-galactic scales.

Abstract

Strong gravitational lensing by galaxies provides us with a unique opportunity to understand the nature of gravity on galactic and extra-galactic scales. In this paper, we propose a new multimessenger approach using data from both gravitational wave (GW) and the corresponding electromagnetic (EM) counterpart to infer the constraint of the modified gravity (MG) theory denoted by the scale dependent phenomenological parameter. To demonstrate the robustness of this approach, we calculate the time-delay predictions by choosing various values of the phenomenological parameters and then compare them with that from the general relativity (GR). For the third generation ground-based GW observatory, with one typical strongly lensed GW+EM event, and assuming that the dominated error from the stellar velocity dispersions is 5\%, the GW time-delay data can distinguish an 18\% MG effect on a scale of tens of kiloparsecs with a $68\%$ confidence level. Assuming GR and a Singular Isothermal Sphere mass model, there exists a simplified consistency relationship between time-delay and imaging data. This relationship does not require for the velocity dispersion measurement, and hence can avoid major uncertainties. By using this relationship, the multimessenger approach is able to distinguish an $8\%$ MG effect. Our results show that the GW multimessenger approach can play an important role in revealing the nature of gravity on the galactic and extra-galactic scales.