Accelerating the standard siren method: Improved constraints on modified gravitational-wave propagation with future data

¹ Dipartimento di Fisica e Astronomia “Augusto Righi”–Università di Bologna, Via Piero Gobetti 93/2, I-40129 Bologna, Italy
² INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
³ INFN – Sezione di Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy

^⋆ Corresponding author: matteo.tagliazucchi2@unibo.it

Received: 28 March 2025
Accepted: 26 August 2025

Abstract

Gravitational waves (GWs) from compact binary mergers have emerged as one of the most promising probes of cosmology and general relativity (GR). However, a major challenge in fully exploiting GWs as “standard sirens” with current and future GW observatories is developing efficient and robust codes capable of analyzing the increasing data volumes that are, and will be, acquired. Here, we present CHIMERA 2.0, an advanced computational framework for hierarchical Bayesian inference of cosmological, modified gravity, and population hyperparameters using standard sirens and galaxy catalogs. This upgrade introduces novel GPU-accelerated algorithms to estimate the hierarchical likelihood, enabling the analysis of thousands of events – crucial for next-generation experiments – and includes the two-parameter (Ξ₀ − n) modified GW propagation model, where Ξ₀ governs the amplitude of the modification (Ξ₀ = 1 corresponds to GR). Using CHIMERA 2.0, we forecast cosmological and modified GW propagation constraints for a scenario similar to the future LIGO-Virgo-KAGRA O5 run. We analyze three binary black-hole populations of 300 events at S/N > 20, each with a different value of Ξ₀: 0.6, 1 (corresponding to GR), and 1.8. Multiple analyses were performed each catalog, comprising a population of approximately 5000 events, thanks to CHIMERA 2.0, which is 10–1000 times faster depending on the settings and catalog size. We jointly infer cosmological, modified GW propagation, and population hyperparameters. With spectroscopic galaxy catalogs, the fiducial Ξ₀ is recovered with a precision of 22%, 7.5%, and 10% for Ξ₀ = 0.6, 1, and 1.8, respectively; while the precision on H₀ is 2 − 7 times worse than when Ξ₀ is not inferred. Finally, in the case of photometric redshifts the constraints degrade on average by 3.5 times in all cases, underscoring the importance of future spectroscopic surveys in maximizing the constraining power of standard sirens.