Gravitational collapse in an expanding background and the role of substructure II: Excess power at small scales and its effect of collapse of structures at larger scales

TL;DR

This study uses N-Body simulations to analyze how small-scale clumping influences large-scale structure formation, finding that effects are minimal if large-scale non-linearity exceeds inter-particle separation.

Contribution

It quantifies the impact of small-scale haloes on large-scale perturbations and assesses detectability of initial power spectrum features in non-linear regimes.

Findings

Small-scale clumping has negligible effect on large-scale evolution.

Features in initial power spectrum are detectable in linear regimes.

Ignoring small-scale perturbations is valid when large-scale non-linearity exceeds inter-particle distance.

Abstract

We study the interplay of clumping at small scales with the collapse and relaxation of perturbations at larger scales using N-Body simulations. We quantify the effect of collapsed haloes on perturbations at larger scales using two point correlation function, moments of counts in cells and mass function. The purpose of the study is twofold and the primary aim is to quantify the role played by collapsed low mass haloes in the evolution of perturbations at large scales, this is in view of the strong effect seen when the large scale perturbation is highly symmetric. Another reason for this study is to ask whether features or a cutoff in the initial power spectrum can be detected using measures of clustering at scales that are already non-linear. The final aim is to understand the effect of ignoring perturbations at scales smaller than the resolution of N-Body simulations. We find that these effects are ignorable if the scale of non-linearity is larger than the average inter-particle separation in simulations. Features in in the initial power spectrum can be detected easily if the scale of these features is in the linear regime, detecting such features becomes difficult as the relevant scales become non-linear. We find no effect of features in initial power spectra at small scales on the evolved power spectra at large scales. We may conclude that in general, the effect on evolution of perturbations at large scales of clumping on small scales is very small and may be ignored in most situations.