Report on 2011.04979v1

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 meanfield 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 10 % up to wave numbers k 10 h 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 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.SciPost Physics Submission 4.2 Damping within Burgers' approximation 10 4.3 Averaged interaction term 11 4.4 Non-linear density-fluctuation power spectrum 12 5 Summary and conclusion 14 A Particle Trajectories 15 A.1 Particle mass 15 A.2 Solution of the Hamiltonian equations of motion 16 A.3 Reference Trajectories 16 A.4 Unifying Propagators 17 B Convolving the particle-particle force with the power spectrum 18 References 19 1 Introduction Kinetic Field Theory (KFT) describes ensembles of classical particles in and out of equilibrium [1-3].It is based upon the Martin-Siggia-Rose approach to classical statistical systems [4] and has been adapted to cosmological initial conditions and to the expanding cosmological background in previous papers [5,6].Its central mathematical object is a generating functional encapsulating the statistical properties of the initial state, the Green's function or propagator of the equations of motion, and the particle-particle interactions.These interactions are described by an exponential operator acting on the free generating functional.In the conventional approach to statistical field theories, this operator is expanded into a Taylor series, leading to a systematic approach to perturbation theory in terms of Feynman diagrams.In this paper, 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.This results in a numerical, time and scale-dependent factor multiplying the free generating functional.Averaging over a pair of density factors then leads to an approximate, but closed and analytic expression for the non-linear power spectrum of cosmic density fluctuations.The mean-field approximation introduces two parameters, the non-linear scale and an effective viscosity reducing the velocity variance after shell-crossing.Both of them can be calibrated from within KFT itself.With these parameters self-calibrated in this way, our mean-field 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.Alternatively, these parameters can be optimised to further improve the agreement between the non-linear power spectra from our mean-field approximation and from numerical simulations.Doing so, the relative deviation to numerical results for ΛCDM can be lowered to 5 % in the same range of wave numbers.In Sect.2, we discuss the trajectories of Hamiltonian particles in the expanding cosmic space-time.Using results derived in detail in Appendix A, we show that the conventional Zel'dovich approximation

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