Reconstruction of $f(T,\mathcal{T})$ Lagrangian for various cosmological scenarios

TL;DR

This paper reconstructs the $f(T,\,\mathcal{T})$ gravity Lagrangian for various cosmological scenarios, demonstrating models compatible with late-time cosmic acceleration through detailed mathematical and physical analysis.

Contribution

It introduces a reconstruction scheme for $f(T,\,\mathcal{T})$ gravity applicable to multiple cosmological eras and scenarios, including matter coupling and viability analysis.

Findings

Reconstructed models align with late-time accelerated expansion.

Constructed functionals are mathematically viable.

Models match observational parameters like the equation of state.

Abstract

In this paper, we explore a reconstruction scheme in the background of the $f(T,\mathcal{T})$ gravity theory for different cosmological scenarios, where $T$ is the scalar torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor. Using the reconstruction technique $f(T, \mathcal{T})$ Lagrangian is constructed for different cosmological eras such as dust, $\Lambda CDM$, perfect fluid, etc. Both minimal and non-minimal matter-coupled models are considered for this purpose. Different cosmological scenarios such as power law expansion, de-Sitter expansion, etc. have been considered, and using them Lagrangian functionals are constructed. Mathematical viabilities of all the constructed functionals have been investigated. The physical implications of the obtained solutions are discussed in detail. To check the cosmological compatibility of the constructed $f(T,\mathcal{T})$ functionals we have generated plots of important parameters like the equation of state parameter and deceleration parameter. It is seen that the reconstructed models are perfectly compatible with the late-time accelerated expansion of the universe.