Simulation-based marginal likelihood for cluster strong lensing cosmology

TL;DR

This paper introduces a simulation-based method to estimate the marginal likelihood for cluster strong lensing data, enabling more robust cosmological model comparisons by incorporating uncertainties and baryonic effects.

Contribution

It presents a novel approach to approximate the Bayes factor using the posterior distribution of scaling relation parameters, tested on X-ray selected clusters with simulations.

Findings

First estimation of marginal likelihood for cluster lensing using simulations

Assessment of uncertainties from baryonic physics and selection effects

Potential of triaxial mass relations as alternative cosmological tests

Abstract

Comparisons between observed and predicted strong lensing properties of galaxy clusters have been routinely used to claim either tension or consistency with $\Lambda$CDM cosmology. However, standard approaches to such cosmological tests are unable to quantify the preference for one cosmology over another. We advocate approximating the relevant Bayes factor using a marginal likelihood that is based on the following summary statistic: the posterior probability distribution function for the parameters of the scaling relation between Einstein radii and cluster mass, $\alpha$ and $\beta$. We demonstrate, for the first time, a method of estimating the marginal likelihood using the X-ray selected $z>0.5$ MACS clusters as a case in point and employing both N-body and hydrodynamic simulations of clusters. We investigate the uncertainty in this estimate and consequential ability to compare competing cosmologies, that arises from incomplete descriptions of baryonic processes, discrepancies in cluster selection criteria, redshift distribution, and dynamical state. The relation between triaxial cluster masses at various overdensities provide a promising alternative to the strong lensing test.