Developing galaxy-cluster potentials into a cosmological diagnostic

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Successful as the cosmological standard model is, its claim for dark matter and dark energy nonetheless poses hitherto unsolved fundamental questions. One of these questions concerns the possible time evolution of the dark energy, for which so far no clue could be found: The simplest, but at the same time least satisfactory explanation of dark energy from the point of view of particle physics is Einstein's cosmological constant. For our understanding of dark energy, it is fundamentally important to know whether the density of the dark energy is changing on cosmological time scales or not.Perhaps the only population of cosmic objects whose evolution depends sensitively enough on a possible time dependence of dark energy is the population of galaxy clusters. If it were possible to count galaxy clusters reliably enough depending on their distance and on at least one intrinsic parameter, a time evolution of the dark energy could be tracked down with substantially higher accuracy than so far possible.Conventionally, the mass of galaxy clusters is used as an internal parameter to establish the relation between observations and theoretical expectations. However, since the mass is neither directly observable nor can theoretically be predicted sufficiently precisely, this relation must be established by means of empirically calibrated scaling relations. Despite all successes, these relations still scatter so much that they are likely to veil the effects of a time dependence of the dark energy on the galaxy-cluster population.We propose to use the gravitational potential of the galaxy clusters instead of the mass to link observations with theory. As a local, directly measureable quantity, the potential has decisive advantages compared to the mass. Our previous work has shown how all available observables of galaxy clusters can be used to determine the potential and how the statistics of the galaxy-cluster population can be characterized theoretically based solely on the gravitational potential.In the project proposed here, we plan to join and integrate the methods we have so far developed, and to test beginning with realistically simulated data whether the resulting method will in fact reduce the scatter in the cosmological inference in the way expected. First applications to existing data will allow us to prepare for upcoming large surveys.