Non-linear Evolution of Matter Power Spectrum in Modified Theory of Gravity

TL;DR

This paper develops a formalism to compute the non-linear matter power spectrum in modified gravity models, successfully matching N-body results and accounting for GR recovery mechanisms, aiding the study of cosmic acceleration without dark energy.

Contribution

It introduces a versatile formalism for non-linear power spectrum calculation in various modified gravity models, incorporating GR recovery mechanisms and validated against N-body simulations.

Findings

Reproduces N-body results for $f(R)$ gravity.

GR recovery suppresses differences from dark energy models.

Formalism applicable to diverse modified gravity theories.

Abstract

We present a formalism to calculate the non-linear matter power spectrum in modified gravity models that explain the late-time acceleration of the Universe without dark energy. Any successful modified gravity models should contain a mechanism to recover General Relativity (GR) on small scales in order to avoid the stringent constrains on deviations from GR at solar system scales. Based on our formalism, the quasi non-linear power spectrum in the Dvali-Gabadadze-Porratti (DGP) braneworld models and $f(R)$ gravity models are derived by taking into account the mechanism to recover GR properly. We also extrapolate our predictions to fully non-linear scales using the Parametrized Post Friedmann (PPF) framework. In $f(R)$ gravity models, the predicted non-linear power spectrum is shown to reproduce N-body results. We find that the mechanism to recover GR suppresses the difference between the modified gravity models and dark energy models with the same expansion history, but the difference remains large at weakly non-linear regime in these models. Our formalism is applicable to a wide variety of modified gravity models and it is ready to use once consistent models for modified gravity are developed.