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

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.

16 pages, no figure, revised version with new references

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• $f(T,\mathcal{T})$ gravity and cosmology
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• Cosmological and Solar System Consequences of f(R,T) Gravity Models
• Stability of the Einstein static Universe in $f(R,T)$ gravity
• Regular black holes in $f(R)$ gravity coupled to nonlinear electrodynamics
• A periodic varying deceleration parameter in $f(R,T)$ gravity
• Reconstruction, Thermodynamics and Stability of $\Lambda$CDM Model in $f(T,\mathcal{T})$ Gravity
• Coincident f(Q) gravity: black holes, regular black holes and black bounces
• Cosmological reconstruction of $f(T,\mathcal{T})$ Gravity
• Generalization of Regular Black Holes in General Relativity to $f(R)$ Gravity
• Consequences of energy conservation violation: Late time solutions of $\Lambda (T)CDM$ subclass of $f(R,T)$ gravity using dynamical system approach
• Viability of Bianchi type V Universe in $f(R,T)=f_1(R)+f_2(R)f_3(T)$ gravity
• From the early to the late time universe within $f(T,\mathcal{T})$ gravity
• Cosmological consequences and statefinder diagnosis of a non-interacting generalized Chaplygin gas in $f(R,T)$ gravity
• Constraining Bianchi type V universe with recent H(z) and BAO observations in Brans-Dicke theory of gravitation
• Late-time cosmological evolution of a general class of f(R, T) gravity with minimal curvature-matter coupling
• Transitioning scenario of Bianchi-I universe within $f\left(R,T\right)$ formalism
• Spherical Accretion of Matter by Charged Black Holes on f(T) Gravity
• Energy conditions in f(T) gravity with higher-derivative torsion terms
• Charged black hole solutions in $f(R,T)$ gravity coupled to nonlinear electrodynamics
• Gödel and Gödel-type solutions in the Palatini $f(R,T)$ gravity theory