Kinetic field theory: Non-linear cosmic power spectra in the mean-field approximation

We use the recently developed Kinetic Field Theory (KFT) for cosmic structure formation to show how non-linear power spectra for cosmic density fluctuations can be calculated in a mean-field approximation to the particle interactions. Our main result is a simple, closed and analytic, approximate expression for this power spectrum. This expression has two parameters characterising non-linear structure growth which can be calibrated within KFT itself. Using this self-calibration, the non-linear power spectrum agrees with results obtained from numerical simulations to within typically \(\lesssim10\,\%\) up to wave numbers \(k\lesssim10\,h\,\mathrm{Mpc}^{-1}\) at redshift \(z = 0\). Adjusting the two parameters to optimise agreement with numerical simulations, the relative difference to numerical results shrinks to typically \(\lesssim 5\,\%\). As part of the derivation of our mean-field approximation, we show that the effective interaction potential between dark-matter particles relative to Zel'dovich trajectories is sourced by non-linear cosmic density fluctuations only, and is approximately of Yukawa rather than Newtonian shape.