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

TL;DR

The paper tackles the challenge of extracting cosmological and modified gravity constraints from gravitational-wave standard sirens in the era of large data volumes. It introduces CHIMERA 2.0, a GPU-accelerated hierarchical Bayesian framework that uses three KDE-based kernels to efficiently compute the GW likelihood for thousands of events, jointly inferring cosmology, MG propagation (via $Ξ_0$ and $n$), and population hyperparameters. Applying this to mock O5-like catalogs with spectroscopic and photometric galaxy redshifts, the study demonstrates that $H_0$ and $Ξ_0$ can be recovered without bias in spectroscopic scenarios, with $Ξ_0$ precision of roughly 22%, 7.5%, and 10% for the three MG cases, while photometric redshifts significantly degrade constraints. The results underscore the importance of spectroscopic surveys for maximizing standard siren constraints and show that CHIMERA 2.0’s GPU-accelerated, multi-kernel approach will be essential for handling next-generation GW data volumes, with planned extensions to real data, larger catalogs, and future detectors.

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. We present here 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 ($Ξ_0-n$) modified GW propagation model. Using CHIMERA 2.0, we forecast cosmological and modified GW propagation constraints for the future LIGO-Virgo-KAGRA O5-like run. We analyze three binary black hole populations of 300 events at SNR>20, each with a different value of $Ξ_0$: 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 $Ξ_0$ is recovered with a precision of $22\%$, $7.5\%$, and $10\%$ for $Ξ_0$ = 0.6, 1, and 1.8, respectively; while the precision on $H_0$ is 2-7 times worse than when $Ξ_0$ 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.

Figures (10)

• Figure 1: Top: Pixelization of 90% localization area of a mock GW event, with PE samples (marked with a cross) colored according to the pixel they fall into. Bottom: Different GW kernels implemented in chimera 2.0. Each line represents the GW kernel in a pixel of the above mock GW event. Kernels are computed at single hyperparameter space points.
• Figure 2: Top: Likelihood evaluation times for catalogs with different numbers of events (each with 5000 PE samples) at a single hyperparameter space point, compared across different kernel algorithms. Solid curves show times on four Intel CPUs (2.0 GHz clock frequency), while dashed curves represent times on a single Nvidia A100 GPU. Bottom: Run times for a full affine-invariant MCMC fit, using the emcee sampler with 50 walkers, on 25 CPUs (left panel) or one GPU (right panel).
• Figure 3: Histograms of galaxy-catalog redshifts (right) and of corresponding luminosity distances in the three MG scenarios considered in this work (left). $\texttt{MG}0.6$ is the sample with $\Xi_0 = 0.6$, $\texttt{GR}$ with $\Xi_0 = 1$, and $\texttt{MG}1.8$ with $\Xi_0 = 1.8$
• Figure 4: Properties of three GW mock catalogs. From left to right: primary mass distributions, redshift distributions, luminosity distance, localization area uncertainties, and histograms of the number of galaxies in the localization volume.
• Figure 5: Marginalized posterior distributions for selected hyperparameters. These constraints are obtained in the first MCMC configuration (inference on all hyperparameters) and assuming a spectroscopic (left panel) or photometric (right panel) galaxy catalog. The colored areas under each posterior represent the 68% C.L. The dotted lines indicate the hyperparameter fiducial values.