Modified f(R) gravity from scalar-tensor theory and inhomogeneous EoS dark energy

TL;DR

This paper explores reconstructing f(R) gravity via scalar-tensor theory and demonstrates its equivalence to a perfect fluid with an inhomogeneous equation of state, shedding light on cosmic acceleration mechanisms.

Contribution

It provides a method to reconstruct f(R) gravity from cosmological evolution and clarifies its equivalence to inhomogeneous fluid models.

Findings

Reconstruction of f(R) from the Hubble parameter evolution.

Mathematical equivalence between f(R) gravity and inhomogeneous fluid models.

Insight into the origin of cosmic acceleration mechanisms.

Abstract

The reconstruction of f(R)-gravity is showed by using an auxiliary scalar field in the context of cosmological evolution, this development provide a way of reconstruct the form of the function f (R) for a given evolution of the Hubble parameter. In analogy, f(R)-gravity may be expressed by a perfect fluid with an inhomogeneous equation of state that depends on the Hubble parameter and its derivatives. This mathematical equivalence that may confuse about the origin of the mechanism that produces the current acceleration, and possibly the whole evolution of the Hubble parameter, is shown here.