Simulation-based marginal likelihood for cluster strong lensing cosmology

Understand

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.