Linear Perturbations Spectra For Dynamical Dark Energy Inspired By Modified Gravity

In this paper, we study a particular modified gravity Equation of State (EoS), 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 1σ) with the ACDM, while at perturbative level, we note that the matter power spectrum normalisation factor σ8 shows an agreement with SDSS and SNeIa+IRAS at 1-σ for the Starobinsky model and with SDSS-vec for the Hu-Sawicki and Exponential models. Furthermore, we found that for the H0 values, Starobinsky and Hu-Sawicki show the least tension in comparison with PL18 TT. All these aspects cannot be observed directly from other alternatives theories, where an equation of state is difficult to compute analytically.