Reconstruction of $f(R)$ Gravity from Cosmological Unified Dark Fluid Model

TL;DR

This paper reconstructs an $f(R)$ gravity model from a unified dark fluid cosmology, analyzing its viability for early universe inflation and comparing its predictions with Planck-2018 data.

Contribution

It provides a novel reconstruction of $f(R)$ gravity from a dark fluid model, linking scalar-tensor theory with cosmological evolution and inflation.

Findings

The reconstructed $f(R)$ model fits Planck-2018 data for certain parameters.

The model can describe both early inflation and late-time acceleration.

The scalar field potential aligns with slow-roll inflation requirements.

Abstract

In this work, we reconstruct the cosmological unified dark fluid model proposed previously by Elkhateeb \cite{Elkhateeb:2017oqy} in the framework of $f(R)$ gravity. Utilizing the equivalence between the scalar-tensor theory and the $f(R)$ gravity theory, the scalar field for the dark fluid is obtained, whence the $f(R)$ function is extracted and its viability is discussed. The $f(R)$ functions and the scalar field potentials have then been extracted in the early and late times of asymptotically de Sitter spacetime. The ability of our function to describe early time inflation is also tested. The early time scalar field potential is used to derive the slow roll inflation parameters. Our results of the tensor-to-scalar ratio $r$ and the scalar spectral index $n_s$ are in good agreement with results from Planck-2018 TT+TE+EE+lowE data for the model parameter $m > 2$.