From the early to the late time universe within $f(T,\mathcal{T})$ gravity

TL;DR

This paper reconstructs $f(T,\,\mathcal{T})$ gravity models to describe the universe's evolution from inflation to late-time acceleration, focusing on a decomposed form of the function and specific scale factor behaviors.

Contribution

It introduces a reconstruction scheme for $f(T,\mathcal{T})$ gravity with a sum of functions, linking theoretical models to different cosmic evolution phases.

Findings

Models can describe universe evolution from inflation to dark energy domination.

Reconstruction based on specific scale factor expressions.

Demonstrates viability of $f(T,\mathcal{T})$ models for cosmic history.

Abstract

In this paper we perform the reconstruction scheme of the gravitational action within $f(T,\mathcal{T})$ gravity, where $T$ and $\mathcal{T}$ denote the torsion scalar and the trace of the energy momentum tensor, respectively. We particularly focus our attention on the case where the algebraic function $f(T,\mathcal{T})$ is decomposed as a sum of two functions $f_1(T)$ and $f_2(\mathcal{T})$, i.e, $f(T,\mathcal{T})=f_{1}(T)+f_{2}(\mathcal{T})$. The description is essentially based on the scale factor and then, we consider two interesting and realistic expressions of this parameter and reconstruct the action corresponding to each phase of the universe. Our results show that some $f(T,\mathcal{T})$ models are able to describe the evolution of the universe from the inflation phase to the late time dark energy dominated phase.