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

TL;DR

This paper introduces a simple, analytic mean-field approximation within Kinetic Field Theory to accurately compute non-linear cosmic power spectra, matching numerical simulations within 5-10% accuracy.

Contribution

It provides a novel, closed-form analytic expression for non-linear cosmic power spectra using a self-calibrated mean-field approach in KFT.

Findings

Achieves <10% accuracy with initial calibration

Reduces discrepancy to <5% after parameter tuning

Reveals effective interaction potential is Yukawa-like

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 $\lesssim10\,\%$ 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.