High accuracy on $H_0$ constraints from gravitational wave lensing events

TL;DR

This paper proposes a novel method using gravitational wave lensing events to constrain the Hubble constant with high accuracy, potentially addressing the Hubble tension by combining gravitational wave and electromagnetic observations.

Contribution

It introduces a new approach to measure the Hubble constant through gravitational lensing of gravitational waves, utilizing wave optics and geometrical optics approximations for different signals.

Findings

Single lensing events can constrain H_0 with uncertainties comparable to current methods.

Combining gravitational wave lensing with Planck priors improves H_0 measurement accuracy.

Method could be decisive in solving the Hubble tension.

Abstract

In light of the newly opened and rapidly growing gravitational waves window in multi-messenger astronomy, in order to fully take advantage of the new opportunities we are provided with, new ideas are required for a better and deeper employ of the state-of-the-art probes we handle. Following this goal, here we suggest a method to constrain the cosmological background, and the Hubble constant in particular, by future observations of gravitationally lensed radiation emitted by a single source in both the gravitational wave and the electromagnetic regimes. The lensing of the gravitational wave radiation, in fact, can leave a clear imprinting in the corresponding waveform, and we want to analyze if such kind of measurements can be successfully employed to better constrain the cosmological background. Thus, by making use of wave optics for the gravitational wave lensed signal, and of standard geometrical optics approximation for the electromagnetic one, we study the impact of different cosmological parameters on the value of the arrival time delay due to gravitational lensing, given specific gravitational wave frequencies, mass models of the lens, and redshifts and positions (with respect to the lens) of the source. Although the rate of lensing of gravitational waves is expected to be low, we show that even one single lensing event, combined with a prior on $\Omega_m$ from \textit{Planck}, could provide us with an uncertainty on $H_0$ comparable with present independent probes in a "pessimistic" scenario (with a pulsar population similar to present Pulsar Timing Array state), and of two orders smaller in an optimistic one (with a number of observed pulsars as large as that expected from the Square Kilometer Array). Thus, its role in the solution of the Hubble tension could be decisive.