Energy conditions in $F(T,\Theta)$ gravity and compatibility with a stable de Sitter solution

TL;DR

This paper explores a modified teleparallel gravity model $F(T,\Theta)$, analyzing its stability, especially of the de Sitter solution, and examines the energy conditions to assess its physical viability.

Contribution

It introduces a new $F(T,\Theta)$ gravity model, derives stability conditions for de Sitter solutions, and investigates the energy conditions within this framework.

Findings

Derived stability conditions for de Sitter solutions.

Identified parameter constraints ensuring stability.

Analyzed energy conditions in the $F(T,\Theta)$ gravity context.

Abstract

We study a new type of the modified teleparallel gravity of the form $F(T,\,\Theta)$ in which $T$, the torsion scalar, is coupled with $\Theta$, the trace of the stress-energy tensor. In a perturbational approach, we study the stability of the solutions and as a special case we find a condition for stability of the de Sitter phase. Then we adopt a suitable form for $F(T,\Theta)$ that realizes a stable de Sitter solution so that the stability condition creates a specific constraint on the parametric space of the model. Finally, the energy conditions in the framework of $F(T,\Theta)$ gravity is investigated.