Non-linear cosmic structure formation in the mean-field approximation

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Understanding the formation of non-linear cosmic structures is important not only because the analysis of current and upcoming data depends on it, but also because these structures in reality as well as in simulations reveal signs of universality whose origin is unclear. Recently, a new analytic approach to non-linear structure formation in classical particle systems in and out of equilibrium has been developed, based on kinetic field theory (KFT). This approach avoids the shell-crossing problem of more conventional approaches by construction and thus allows to enter quite deeply into the non-linear regime even at low orders of perturbation theory. In addition, a mean-field approximation has been developed within KFT that reproduces non-linear power spectra of numerically simulated cosmic density fluctuations at the per-cent level in a wide range of wave numbers in the trans-linear and non-linear regimes. This mean-field approximation has so far been derived in a heuristic way. Motivated by its success, the present proposal aims at clarifying its foundations, placing it on a rigorous derivation, and extending it towards spectra of higher order, such as the bi- or trispectrum. The work programme foresees developing probability distributions for finding particles correlated with the mean density field in evolved ensembles of classical particles out of equilibrium under appropriately realistic approximations, averaging interaction terms in the generating functional of KFT with these probability distributions, and deriving power spectra, bispectra, and possibly trispectra. It further foresees studying how the Hubbard-Stratonovich transformation could be introduced into KFT in a cosmological context, and how this transformation could be used to further understand and develop the mean-field approximation to cosmic structure formation. This approach will also allow to extend studies of non-linear cosmic structures to non-standard cosmological models or theories of gravity.