Perturbation theory with dispersion and higher cumulants: non-linear regime

Abstract

We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering of collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. We show that VPT can be cast into a form that is formally analogous to standard perturbation theory (SPT), but including additional perturbation variables, non-linear interactions, and a more complex propagation. VPT non-linear kernels have a crucial decoupling property: for fixed total momentum, the kernels becomes strongly suppressed when any of the individual momenta cross the dispersion scale into the non-linear regime. This screening of UV modes allows us to compute non-linear corrections to power spectra even for cosmologies with very blue power-law input spectra, for which SPT diverges. We compare predictions for the density and velocity divergence power spectra as well as the bispectrum at one-loop order to N-body results in a scaling universe with spectral indices $-1\le n_s\le +2$. We find a good agreement up to the non-linear scale for all cases, with a reach that increases with the spectral index $n_s$. We discuss the generation of vorticity as well as vector and tensor modes of the velocity dispersion, showing that neglecting vorticity when including dispersion would lead to a violation of momentum conservation. We verify momentum conservation when including vorticity, and compute the vorticity power spectrum at two-loop order, necessary to recover the correct large-scale limit with slope $n_w=2$. Comparing to our N-body measurements confirms the cross-over from $k^4$ to $k^2$ scaling on large scales. Our results provide a proof-of-principle that perturbative techniques for dark matter clustering can be systematically improved based on the known underlying collisionless dynamics.

37 pages + appendices, 23 figures

References in corpus (12)

• Transients from Initial Conditions in Cosmological Simulations
• A universal model for halo concentrations
• Generation of Vorticity and Velocity Dispersion by Orbit Crossing
• Large-scale dark matter simulations
• The Bispectrum in the Effective Field Theory of Large Scale Structure
• Linear perturbative theory of the discrete cosmological N-body problem
• Soft-Pion Theorems for Large Scale Structure
• Quantification of discreteness effects in cosmological N-body simulations: II. Evolution up to shell crossing
• Large-scale structure perturbation theory without losing stream crossing
• Moving around the cosmological parameter space: a nonlinear power spectrum reconstruction based on high-resolution cosmic responses
• The two-loop bispectrum of large-scale structure
• Perturbation theory with dispersion and higher cumulants: framework and linear theory

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