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Weighted ABC: a new strategy for cluster strong lensing cosmology with simulations [Replacement]

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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 using a `weighted' variant of approximate Bayesian computation (ABC), whereby the posterior probability distribution function for the parameters of the scaling relation between Einstein radii and cluster mass, $\alpha$ and $\beta$, is treated as the summary statistic. We demonstrate, for the first time, a method of estimating the evidence (a.k.a. the marginal likelihood) under the $\Lambda$CDM framework, 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. Essentially, the summary statistic is calculated for both data and the average of several simulated datasets, and the evidence is the cross-correlation of the two PDFs. We investigate the uncertainty in the calculated evidence 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.


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