This document was submitted as supporting material to an Engineering Change Proposal (ECP) for the Square Kilometre Array (SKA). This ECP requests gridded visibilities as an extra imaging data product from the SKA, in order to enable bespoke analysis
techniques to measure source morphologies to the accuracy necessary for precision cosmology with radio weak lensing. We also discuss the properties of an SKA weak lensing data set and potential overlaps with other cosmology science goals.
We consider methods with which to answer the question is any observed galaxy cluster too unusual for Lambda-CDM? After emphasising that many previous attempts to answer this question will overestimate the confidence level at which Lambda-CDM can be r
uled out, we outline a consistent approach to these rare clusters, which allows the question to be answered. We define three statistical measures, each of which are sensitive to changes in cluster populations arising from different modifications to the cosmological model. We also use these properties to define the equivalent mass at redshift zero for a cluster --- the mass of an equally unusual cluster today. This quantity is independent of the observational survey in which the cluster was found, which makes it an ideal proxy for ranking the relative unusualness of clusters detected by different surveys. These methods are then used on a comprehensive sample of observed galaxy clusters and we confirm that all are less than 2-sigma deviations from the Lambda-CDM expectation. Whereas we have only applied our method to galaxy clusters, it is applicable to any isolated, collapsed, halo. As motivation for future surveys, we also calculate where in the mass redshift plane the rarest halo is most likely to be found, giving information as to which objects might be the most fruitful in the search for new physics.
Motivated by recent suggestions that a number of observed galaxy clusters have masses which are too high for their given redshift to occur naturally in a standard model cosmology, we use Extreme Value Statistics to construct confidence regions in the
mass-redshift plane for the most extreme objects expected in the universe. We show how such a diagram not only provides a way of potentially ruling out the concordance cosmology, but also allows us to differentiate between alternative models of enhanced structure formation. We compare our theoretical prediction with observations, placing currently observed high and low redshift clusters on a mass-redshift diagram and find -- provided we consider the full sky to avoid a posteriori selection effects -- that none are in significant tension with concordance cosmology.
