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

Takahiro Nishimichi,Francis Bernardeau,Atsushi Taruya

doi:10.1016/j.physletb.2016.09.035

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.

Highlights

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 selfgravitating 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
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
We have presented the first direct measurement of the response function that governs the dependence of the nonlinear power spectrum on the initial spectrum during cosmic structure formation

Summary

Methodology

We prepare two initial conditions with small modulations in the linear spectrum over a finite interval of wave mode q, evolve them to a late time, and take the difference of the nonlinear spectra measured from the two. Since we can check the dependence of the response function on the overall amplitude of the power spectrum by looking at the results at different redshifts, we here focus on the variety in only the shape of the spectrum. Covering different wave number intervals, these simulations allow us to examine the convergence of the measured response function. For each set of simulations, we prepare multiple initial conditions with linear spectra perturbed by ±1% over qj ≤ q < qj+1. Since the estimator (2) takes the difference of the two spectra, this helps us to reduce the statistical scatter on the response function significantly

Shape of the response function and comparison with PT

Findings

Discussion

Summary