Response function of the large-scale structure of the universe to the small scale inhomogeneities

TL;DR

This study measures the response function of the universe's large-scale structure to small-scale inhomogeneities using cosmological simulations, revealing insensitivity to small-scale physics and informing perturbation theory limits.

Contribution

First measurement of the response function of large-scale structure to small-scale inhomogeneities using N-body simulations, validating perturbation theory predictions and identifying damping effects.

Findings

Response function agrees with perturbation theory except for small-to-large scale coupling.

Small-scale physics has minimal impact on large-scale statistical properties.

Damping of small-to-large scale coupling follows a Lorentzian form.

Abstract

In order to infer the impact of the small-scale physics to the large-scale properties of the universe, we use a series of cosmological $N$-body simulations of self-gravitating matter inhomogeneities to measure, for the first time, the response function of such a system defined as a functional derivative of the nonlinear power spectrum with respect to its linear counterpart. Its measured shape and amplitude are found to be in good agreement with perturbation theory predictions except for the coupling from small to large-scale perturbations. The latter is found to be significantly damped, following a Lorentzian form. These results shed light on validity regime of perturbation theory calculations giving a useful guideline for regularization of small scale effects in analytical modeling. Most importantly our result indicates that the statistical properties of the large-scale structure of the universe are remarkably insensitive to the details of the small-scale physics, astrophysical or gravitational, paving the way for the derivation of robust estimates of theoretical uncertainties on the determination of cosmological parameters from large-scale survey observations.