Abstract
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.
Highlights
We briefly review the Kinetic Field Theory (KFT) approach to cosmic structure formation
We have previously shown that even the first order of this perturbative approach leads to non-linear density-fluctuation power spectra close to results from numerical simulations [5], and we will further analyse KFT perturbation theory in future papers
Before we proceed to construct and analyse such an average, we briefly review how power spectra are derived in KFT from the generating functional Z[J]
Summary
Kinetic Field Theory (KFT) describes ensembles of classical particles in and out of equilibrium [1,2,3]. Unlike other approaches to kinetic theory, KFT is not based on a phase-space density function subject to the Liouville or Boltzmann equations It is a kinetic theory in the sense that it describes the joint evolution of a particle ensemble while intentionally integrating over microscopic information. We show that the interaction operator can instead be approximated as an averaged interaction term using a mean-field approach This can be done in such a way that its action on the generating functional can be separated from the integration over the initial phase-space distribution. Both of them can be calibrated from within KFT itself With these parameters self-calibrated in this way, our meanfield approximation to the non-linear power spectrum agrees with results from numerical simulations with a relative deviation of typically 10% up to k ≈ 10 h Mpc−1 at redshift z = 0.
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