Cosmological reconstruction of $f(T,\mathcal{T})$ Gravity

Abstract

Motivated by the newly proposal for gravity as the effect of the torsion scalar $T$ and trace of the energy momentum tensor $\mathcal{T}$,we investigate the cosmological reconstruction of different models of the Universe. Our aim here is to show that how this modified gravity model, $f(T,\mathcal{T})$ is able to reproduce different epoches of the cosmological history. We explicitly show that $f(T,\mathcal{T})$ can be reconstructed for $\Lambda$CDM as the most popular and consistent model. Also we study the mathematical reconstruction of $f(T,\mathcal{T})$ for a flat cosmological background filled by two fluids mixture. Such model describes phantom-non-phantom era as well as the purely phantom cosmology. We extend our investigation to more cosmological models like perfect fluid,Chaplygin gas and massless scalar field. In each case we obtain some specific forms of $f(T,\mathcal{T})$. These families of $f(T,\mathcal{T})$ contain arbitrary function of torsion and trace of the energy momentum.

references added, Accepted for publication in "International Journal of Geometric Methods in Modern Physics."

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• Teleparallel Gravity: From Theory to Cosmology
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• Gravastars in $f(\mathbb{T},\mathcal{T})$ gravity
• Constraining $f(T,\mathcal{T})$ gravity models using type Ia supernovae
• From the early to the late time universe within $f(T,\mathcal{T})$ gravity
• Cosmological models in $f(T,\mathcal{T})$ gravity and the dynamical system analysis
• Modelling of a compact anisotropic star as an anisotropic fluid sphere in $f(T)$ gravity
• First-order formalism for thick branes in $f(T,\mathcal{T})$ gravity
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Geodesic Congruences and a Collapsing Stellar Distribution in f (T ) Theories
• Slow-roll inflation in $f(T,\mathcal{T})$ modified gravity
• Non-singular bouncing cosmology in $f(T,\mathcal{T})$ gravity with energy condition violations
• Late Time Phenomena in $f(T,\mathcal{T})$ Gravity Framework: Role of $H_0$ Priors
• Holographic dark energy reconstruction of $f(T,\mathcal{T})$ gravity
• Noether symmetry in $F(T)$ gravity with $f$-essence