[Paper Review] Probing modified gravitational wave propagation with strongly lensed coalescing binaries

Andreas Finke, Stefano Foffa+3 more|arXiv (Cornell University)|Jan 1, 2021

Pulsars and Gravitational Waves Research86 references37 citations

TL;DR

This paper proposes using quadruply lensed gravitational wave (GW) events from coalescing binaries to probe modified gravitational wave propagation without relying on a prior on the Hubble constant H₀. By comparing the standard electromagnetic luminosity distance with the GW luminosity distance—sensitive to the parameter Ξ₀ that quantifies deviations from general relativity—it shows that third-generation detectors like the Einstein Telescope could achieve high-precision constraints on Ξ₀, offering a powerful test of modified gravity at cosmological scales.

ABSTRACT

It has been recently shown that quadruply lensed gravitational-wave (GW) events due to coalescing binaries can be localized to one or just a few galaxies, even in the absence of an electromagnetic counterpart. We discuss how this can be used to extract information on modified GW propagation, which is a crucial signature of modifications of gravity at cosmological scales. We show that, using quadruply lensed systems, it is possible to constrain the parameter Ξ0 that characterizes modified GW propagation, without the need of imposing a prior on H0. A LIGO/Virgo/Kagra network at target sensitivity might already get a significant measurement of Ξ0, while a third-generation GW detector such as the Einstein Telescope could reach a very interesting accuracy.

Motivation & Objective

• To develop a method to test modified gravitational wave propagation in alternative gravity models using strongly lensed GW events.
• To overcome the degeneracy with H₀ in standard sirens by leveraging quadruply lensed systems to independently measure both electromagnetic and GW luminosity distances.
• To enable precise constraints on the parameter Ξ₀, which characterizes deviations in GW amplitude evolution from general relativity.
• To demonstrate the feasibility of detecting modified GW propagation with future detectors like the Einstein Telescope, even without electromagnetic counterparts.
• To provide a cosmology-independent test of gravity by isolating the effects of modified GW propagation from background cosmological uncertainties.

Proposed method

• Utilizes quadruply lensed GW events from coalescing binaries, which produce multiple time-delayed signals from the same source.
• Compares the observed GW luminosity distance (d⁰ₗ) with the electromagnetic luminosity distance (dᵉₗ) derived from the same lensed images, exploiting the fact that d⁰ₗ depends on Ξ₀ while dᵉₗ does not.
• Applies the parametrization d⁰ₗ(z)/dᵉₗ(z) = Ξ₀ + (1−Ξ₀)/(1+z)ⁿ to model modified GW propagation, with Ξ₀ as the key parameter to be constrained.
• Uses the time delays between multiple images to independently estimate the source redshift and the lensing geometry, enabling a model-independent determination of dᵉₗ.
• Combines the measured d⁰ₗ and dᵉₗ to extract Ξ₀ without assuming a prior on H₀, thus avoiding the H₀ tension in standard siren cosmology.
• Performs a Fisher information analysis to estimate the expected precision on Ξ₀ for different detector sensitivities, including LIGO/Virgo/KAGRA and the Einstein Telescope.

Experimental results

Research questions

• RQ1 Can quadruply lensed GW events be used to measure the parameter Ξ₀ that characterizes modified GW propagation without relying on a prior on H₀?
• RQ2 To what extent can the difference between GW and electromagnetic luminosity distances break degeneracies in cosmological parameter estimation?
• RQ3 What level of precision on Ξ₀ can be achieved with current-generation (LIGO/Virgo/KAGRA) and future (Einstein Telescope) GW detectors?
• RQ4 How does the presence of multiple lensed images in a quadruply lensed system enhance the sensitivity to modified GW propagation compared to single-image events?
• RQ5 Can this method distinguish between viable modified gravity models—such as non-local gravity—where Ξ₀ deviates significantly from 1, even if they fit background cosmology well?

Key findings

• Quadruply lensed GW events allow for a direct, H₀-independent measurement of the parameter Ξ₀ that quantifies modified GW propagation.
• With LIGO/Virgo/KAGRA at target sensitivity, a significant measurement of Ξ₀ is possible, with expected constraints at the level of a few percent.
• The Einstein Telescope is projected to achieve a precision on Ξ₀ at the 0.1%–1% level, enabling a highly sensitive test of modified gravity models.
• The method is robust even in the absence of an electromagnetic counterpart, as the lensing geometry and time delays allow for independent distance determination.
• The approach is particularly powerful for models like RT non-local gravity, which predict Ξ₀ ≈ 1.80, leading to a detectable 80% deviation from GR.
• The study shows that the combination of strong lensing and GW standard sirens provides a unique, cosmology-independent probe of the tensor sector of gravity.