Non-linear evolution of cosmological power-spectra using kinetic field theory approach

We use the kinetic field theory approach to study the evolution of simple primordial power spectra and related higher order correlators. Kinetic field theory is a microscopic, non equilibrium statistical field theory that can be accustomed to treat large scale structure formation. Due to its features, it overcomes some difficulties arising in other perturbative approaches, the most famous being shell crossing. In particular, we will use a non-perturbative approach we call Born approximation, that involves a suitable averaging procedure to include gravitational interactions, to probe the non linear evolution of some class of simplified primordial power spectra; one class will be related to the dark matter primordial power spectrum but with a changing small scale slope. We will also analyze Gaussian shape primordial power spectra; such spectra are cosmologically irrelevant, but nevertheless it is interesting to see what kinetic field theory predicts also for such cases. We found that all these evolved power spectra have a small scale fall-off that goes as k^-3 , where k is the wavenumber; this behavior seems thus to be valid for a wide class of non-linearly evolved primordial power spectra. Another goal of this work is to analyze higher order correlators (like the bispectrum) evolution within this framework.