Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations

TL;DR

This paper introduces a differential equation-based method for computing nonlinear cosmological power spectra and higher order correlations, adaptable to various cosmologies and validated against simulations.

Contribution

The authors present a novel differential equation approach for nonlinear cosmological perturbations, extending resummation techniques and applicable beyond standard LambdaCDM models.

Findings

Accurately computes BAO features in the power spectrum.

Velocity spectra are less affected by nonlinearities.

Method agrees well with N-body simulations and other models.

Abstract

Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order correlations, are obtained -- at any redshift and for any momentum scale -- by integrating a system of differential equations. The method is similar to the familiar BBGKY hierarchy. Truncating at the level of the trispectrum, the solution of the equations corresponds to the summation of an infinite class of perturbative corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than LambdaCDM, such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the Baryonic Acoustic Oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density-velocity and velocity-velocity power spectra are also computed, showing that they are much less contaminated by nonlinearities than the density-density one. The approach can be seen as a particular formulation of the renormalization group, in which time is the flow parameter.