The impact of strong lensing on Hubble constant measurements with gravitational-wave dark sirens

Abstract

The disagreement between early and late Universe electromagnetic measurements of the Hubble constant, $H_0$, known as the Hubble tension, highlights the need for independent and complementary probes. Gravitational-wave events have recently emerged as such a probe for constraining cosmological parameters. $H_{0}$ inference using these events relies on sky localization and luminosity distance estimates, both of which can be significantly improved for strongly lensed events with appropriate lens modeling. In this context, we propose utilizing strong lensing of dark sirens, gravitational-wave events without identified electromagnetic counterparts, in combination with strong lensing of galaxies as a novel method for measuring $H_0$. The constant is inferred from the luminosity distances of these lensed dark sirens and the redshifts of their host galaxies, combining information from individual events to obtain statistically stronger constraints when multiple events are available. We adopt a simulated galaxy catalog, \texttt{MICECATv2}, as the basis for simulating strong lensing of galaxies and to provide the redshift information of host galaxy candidates required to infer $H_0$. We also examine the impact of galaxy catalog incompleteness on the resulting $H_0$ inference. Our results demonstrate that using only 8 strongly lensed dark sirens, analyzed with a dedicated galaxy-galaxy lensing catalog, can improve the precision of $H_{0}$ by roughly 50\% compared to 250 unlensed events.

Figures (9)

• Figure 1: Left panel: The redshift distribution of galaxies in the unlensed catalog, UGC0 (red), which contains approximately 64 million galaxies. Right panel: The redshift distributions of galaxies in the lensed catalog, LGC0. The number of quadruple-image systems (green) is smaller than that of double-image systems (blue) because the lensing cross-section for quadruple-image formation is much smaller than that for double-image formation.
• Figure 2: Sky localization maps for selected double- and quadruple-image systems. The left (right) panels show double (quadruple) image systems. The top row corresponds to systems with the highest $\rho_{\rm mean}$, which exhibit the most tightly constrained sky localizations, while the bottom row shows systems with the lowest $\rho_{\rm mean}$, showing the broader posterior regions. The black and gray solid contours represent the 50% and 90% credible regions, respectively. The star symbols mark the true sky positions of the corresponding GW lensing systems.
• Figure 3: Distributions of the median relative magnification factors and time delays obtained from EM observations for the source–lens galaxy systems within the localized sky area of each double-image case. The blue and green dashed lines indicate the constrained boundaries of $\mu_{\rm rel, GW}$ and $\Delta t_{\rm GW}$ inferred from the observed lensed GW signals. Blue dots represent lensing systems consistent with the $\mu_{\rm rel, GW}$ constraint, while grey dots denote the systems inconsistent with either constraint. Note that no systems are consistent with only the $\Delta t_{\rm GW}$ constraint because the GW time delays are tightly constrained. Magenta stars indicate systems consistent with both $\mu_{\rm rel, GW}$ and $\Delta t_{\rm GW}$. The inset highlights the error bars on $\mu_{\rm rel, EM}$ and $\Delta t_{\rm EM}$. For the lowest (highest) $\rho_{\rm mean}$ cases, five (one) systems remain consistent with the two GW observables.
• Figure 4: Posteriors of the apparent (orange) and retrieved true (green) luminosity distances for each case, along with the recovered magnification factor (blue), $\mu_{1}$, for the first-arriving lensed GW signal obtained via rejection sampling. Dashed lines indicate the injected values. In all cases, the injections are included within the posteriors, and the uncertainties of the retrieved true distances are notably narrower for quadruple-image systems compared to double-image systems.
• Figure 5: The posteriors of the Hubble constant for Cases 1 and 2 for both double- and quadruple-image systems. The solid dashed line indicates the true value, and the dotted lines denote the 90% credible intervals (C.I.). The blue (orange) solid curve shows the case in which the redshift used to compute the recessional velocity is obtained from spectroscopic (photometric) measurements. Both Cases 1 and 2 of the quadruple-image system show well-constrained posteriors, as the luminosity distances are precisely recovered and the delensing process performs well. In contrast, both Cases 1 and 2 of the double-image system exhibit broader C.I. and peaks that deviate further from the true value due to less effective delensing. In addition, Case 2 of both the double- and quadruple-image systems shows broader C.I. because the precision of distance inference is lower for low-S/N signals.