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

We study a new type of the modified teleparallel gravity of the form F(T,Θ) in which T, the torsion scalar, is coupled with Θ, 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,Θ) 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,Θ) gravity is investigated