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\,\%≲10%
up to wave numbers k\lesssim10\,h\,\mathrm{Mpc}^{-1}k≲10hMpc−1
at redshift z = 0z=0.
Adjusting the two parameters to optimise agreement with numerical
simulations, the relative difference to numerical results shrinks to
typically \lesssim 5\,\%≲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.
Kinetic field theory: Non-linear cosmic power spectra in the mean-field approximation
