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

Understand

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.