Effective dark matter power spectra in $f(R)$ gravity

TL;DR

This study uses N-body simulations to measure the effective dark matter power spectrum in $f(R)$ gravity, revealing significant deviations from the $\\Lambda$CDM model that are underestimated by traditional analyses.

Contribution

It introduces the effective dark matter power spectrum in $f(R)$ gravity and demonstrates its importance for accurately assessing deviations from $\\Lambda$CDM.

Findings

Effective power spectrum deviates over 150% for certain $f(R)$ models.

Traditional matter power spectrum underestimates $f(R)$ effects.

Effective density field can better discriminate $f(R)$ gravity from $\\Lambda$CDM.

Abstract

Using N-body simulations, we measure the power spectrum of the effective dark matter density field, which is defined through the modified Poisson equation in $f(R)$ cosmologies. We find that when compared to the conventional dark matter power spectrum, the effective power spectrum deviates more significantly from the $\Lambda$CDM model. For models with $f_{R0}=-10^{-4}$, the deviation can exceed 150\% while the deviation of the conventional matter power spectrum is less than 50\%. Even for models with $f_{R0}=-10^{-6}$, for which the conventional matter power spectrum is very close to the $\Lambda$CDM prediction, the effective power spectrum shows sizeable deviations. Our results indicate that traditional analyses based on the dark matter density field may seriously underestimate the impact of $f(R)$ gravity on galaxy clustering. We therefore suggest the use of the effective density field in such studies. In addition, based on our findings, we also discuss several possible methods of making use of the differences between the conventional and effective dark matter power spectra in $f(R)$ gravity to discriminate the theory from the $\Lambda$CDM model.