Simulation-based marginal likelihood for cluster strong lensing cosmology

KILLEDAR, M.; BORGANI, S.; FABJAN, D.; DOLAG, K.; GRANATO, G.; MENEGHETTI, M.; PLANELLES, S.; RAGONE-FIGUEROA, C.

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY

WILEY-BLACKWELL PUBLISHING, INC

Año: 2018 vol. 473 p. 1736 - 1750

0035-8711

Comparisons between observed and predicted strong lensing properties of galaxy clusters have been routinely used to claim either tension or consistency with Λ cold dark matter 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, α and β. We demonstrate, for the first time, a method of estimating the marginal likelihood using the X-ray selected z > 0.5 Massive Cluster Survey 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, which 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 provides a promising alternative to the strong lensing test.