Impact of cosmological signatures in two-point statistics beyond the linear regime

TL;DR

This paper investigates how phase transitions in dark-sector energy densities affect the non-linear evolution of cosmological signatures in the matter power spectrum and correlation function, revealing complex damping and modulation effects.

Contribution

It models the non-linear evolution of phase transition signatures using simulations and perturbation theory, focusing on response ratios rather than absolute statistics.

Findings

Non-linearities produce a second bump at smaller scales.

Redshift space signatures are partially erased by particle motions.

Correlation function oscillations are damped by large-scale flows.

Abstract

Some beyond $\Lambda$CDM cosmological models have dark-sector energy densities that suffer phase transitions. Fluctuations entering the horizon during such a transition can receive enhancements that ultimately show up as a distinctive bump in the power spectrum relative to a model with no phase transition. In this work, we study the non-linear evolution of such signatures in the matter power spectrum and correlation function using N-body simulations, perturbation theory and HMcode - a halo-model based method. We focus on modelling the response, computed as the ratio of statistics between a model containing a bump and one without it, rather than in the statistics themselves. Instead of working with a specific theoretical model, we inject a parametric family of Gaussian bumps into otherwise standard $\Lambda$CDM spectra. We find that even when the primordial bump is located at linear scales, non-linearities tend to produce a second bump at smaller scales. This effect is understood within the halo model due to a more efficient halo formation. In redshift space these nonlinear signatures are partially erased because of the damping along the line-of-sight direction produced by non-coherent motions of particles at small scales. In configuration space, the bump modulates the correlation function reflecting as oscillations in the response, as it is clear in linear Eulerian theory; however, they become damped because large scale coherent flows have some tendency to occupy regions more depleted of particles. This mechanism is explained within Lagrangian Perturbation Theory and well captured by our simulations.