Reconstructing $f(R,T)$ gravity from holographic dark energy

TL;DR

This paper reconstructs specific $f(R,T)$ gravity models to replicate the expansion history of the universe as explained by dark matter and holographic dark energy within General Relativity.

Contribution

It introduces a numerical method to reconstruct $f(R,T)$ functions that match the expansion history driven by dark energy models.

Findings

Reconstructed $f(R,T)$ models successfully mimic standard dark energy expansion.

Analyzed two specific $f(R,T)$ models: $R+2f(T)$ and $f(R)+ ext{ extlambda} T$.

Demonstrated the viability of $f(R,T)$ gravity in reproducing cosmological observations.

Abstract

We consider cosmological scenarios based on $f(R,T)$ theories of gravity ($R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor) and numerically reconstruct the function $f(R,T)$ which is able to reproduce the same expansion history generated, in the standard General Relativity theory, by dark matter and holographic dark energy. We consider two special $f(R,T)$ models: in the first instance, we investigate the modification $R + 2f(T)$, i.e. the usual Einstein-Hilbert term plus a $f(T)$ correction. In the second instance, we consider a $f(R)+\lambda T$ theory, i.e. a $T$ correction to the renown $f(R)$ theory of gravity.