Linear perturbations spectra for dynamical dark energy inspired by modified gravity

TL;DR

This paper investigates a modified gravity equation of state that can replicate popular $f(R)$ models, analyzing its cosmological implications and compatibility with observational data, especially in the context of dynamical dark energy and perturbations.

Contribution

It introduces a specific modified gravity equation of state capable of reproducing key $f(R)$ models and assesses its observational viability through perturbation analysis and data comparison.

Findings

The model aligns with $ ext{Lambda}$CDM within $1\sigma$.

Matter power spectrum normalization $\sigma_8$ agrees with observations for certain models.

Starobinsky and Hu-Sawicki models show minimal $H_0$ tension.

Abstract

In this paper, we study a particular modified gravity Equation of State, the so-called Jaime-Jaber-Escamilla, that emerges from the first gravity modified action principle and can reproduce three cosmological viable $f(R)$ theories: the Starobinsky, Hu-Sawicki, and Exponential models . This EoS is a suitable candidate to reproduce the dynamical dark energy behaviour already reconstructed by the current data sets. Based on the joint statistical analysis, we found that our results are still in good agreement (within $1\sigma$) with the $\Lambda$CDM, while at perturbative level we notice that the matter power spectrum normalisation factor $\sigma_8$ shows an agreement with SDSS and SNeIa+IRAS at 1-$\sigma$ for the Starobinsky model and with SDSS-vec for the Hu \& Sawicki and Exponential models. Furthermore, we found that for the $H_0$ values, Starobinsky and Hu \& Sawicki show the least tension in comparison with PL18 TT. All these aspects cannot be observed \textit{directly} from other alternatives theories, were a equation of state is difficult to compute analytically.