Potential fluctuations, cluster physics, and gravitational lensing
Mass is a poorly defined property of cosmological objects such as galaxy clusters because their boundary is not observable. Yet, cosmological information is extracted from the galaxy-cluster population by comparing theoretical mass functions to observed X-ray temperature or luminosity functions. Using the statistics of the gravitational potential instead, it is possible to directly derive theoretical X-ray temperature functions without reference to mass. This will considerably reduce the scatter in the comparison between theoretical and observed cluster distribution functions, and thus tighten cosmological constraints.
The same techniques developed in this context can be used to predict the number of density peaks expected to be detectable for gravitational-lensing experiments. The contamination of such peak counts by spurious detections can be constrained, and thus also the number counts of real dark-matter halos. These predictions are in excellent agreement with numerical simulations. Using
optimised filters for halo detections through gravitational lensing, cosmological constraints through weak-lensing halo counts will become possible.