Reconstructing f(R) model from Holographic DE: Using the observational evidence

TL;DR

This paper explores how a specific $f(R)$ gravity model can be reconstructed from interacting holographic dark energy, aligning with observational evidence like accelerated expansion and thermodynamic laws.

Contribution

It establishes a method to derive a viable $f(R)$ model consistent with observational constraints from holographic dark energy.

Findings

Derived conditions for accelerated expansion and thermodynamic validity.

Reconstructed explicit forms of scalar field, potential, and scale factor.

Proposed a viable $f(R)$ model explaining current universe observations.

Abstract

We investigate the corresponding relation between $f(R)$ gravity and an interacting holographic dark energy. By obtaining conditions needed for some observational evidence such as, positive acceleration expansion of universe, crossing the phantom divide line and validity of thermodynamics second law in an interacting HDE model and corresponding it with $f(R)$ mode of gravity we find a viable $f(R)$ model which can explain the present universe. We also obtain the explicit evolutionary forms of the corresponding scalar field, potential and scale factor of universe.