Cosmological reconstruction of $f(T,\mathcal{T})$ Gravity

TL;DR

This paper explores how the modified gravity model $f(T,\,\mathcal{T})$ can be reconstructed to replicate various cosmological epochs, including $\,\Lambda$CDM, phantom, and scalar field models, demonstrating its versatility in cosmological modeling.

Contribution

It provides explicit reconstruction methods for $f(T,\mathcal{T})$ gravity to match different cosmological scenarios, extending the understanding of this modified gravity framework.

Findings

Reconstructed $f(T,\mathcal{T})$ for $\,\Lambda$CDM model.

Derived forms of $f(T,\mathcal{T})$ for phantom and non-phantom eras.

Extended reconstruction to models with perfect fluid, Chaplygin gas, and scalar fields.

Abstract

Motivated by the newly proposal for gravity as the effect of the torsion scalar $T$ and trace of the energy momentum tensor $\mathcal{T}$,we investigate the cosmological reconstruction of different models of the Universe. Our aim here is to show that how this modified gravity model, $f(T,\mathcal{T})$ is able to reproduce different epoches of the cosmological history. We explicitly show that $f(T,\mathcal{T})$ can be reconstructed for $\Lambda $CDM as the most popular and consistent model. Also we study the mathematical reconstruction of $f(T,\mathcal{T})$ for a flat cosmological background filled by two fluids mixture. Such model describes phantom-non-phantom era as well as the purely phantom cosmology. We extend our investigation to more cosmological models like perfect fluid,Chaplygin gas and massless scalar field. In each case we obtain some specific forms of $f(T,\mathcal{T})$. These families of $f(T,\mathcal{T})$ contain arbitrary function of torsion and trace of the energy momentum.