Revisiting the matter power spectra in $f(R)$ gravity

TL;DR

This study uses high-resolution simulations to analyze the non-linear matter power spectrum in $f(R)$ gravity models, revealing how the chameleon mechanism operates and constrains model parameters based on gravitational modifications.

Contribution

It provides detailed simulation-based analysis of the matter power spectrum in $f(R)$ models and introduces a generalized PPF fitting formula for these models.

Findings

Chameleon mechanism operates in dense regions for $|f_{R0}|<10^{-4}$.

No chameleon screening in dense regions for $|f_{R0}|>10^{-3}$ at late times.

The generalized PPF formula accurately fits the simulated data.

Abstract

In this paper, we study the non-linear matter power spectrum in a specific family of $f(R)$ models that can reproduce the $\Lambda$CDM background expansion history, using high resolution $N$-body simulations based on the {\sc ecosmog} code. We measure the matter power spectrum in the range of $0.05h{\rm Mpc}^{-1}<k<10h{\rm Mpc}^{-1}$ from simulations for our $f(R)$ models and give theoretical explanations to their behaviour and evolution patterns. We also examine the chameleon mechanism for our models and find that it works throughout the cosmic history in dense regions, for our $f(R)$ models with $|f_{R0}|<10^{-4}$. On the other hand, for models with $|f_{R0}|>10^{-3}$, we find no chameleon screening in dense regions at late times ($z<3$), which means that those models could be ruled out due to the factor-of-$1/3$ enhancement to the strength of Newtonian gravity. We also give the best-fit parameters for a generalised PPF fitting formula which works well for the models studied here.