Reconstruction, Thermodynamics and Stability of $\Lambda$CDM Model in $f(T,\mathcal{T})$ Gravity

Understand

We reconstruct the $\Lambda$CDM model for $f(T,\mathcal{T})$ Theory, where $T$ is the torsion scalar and $\mathcal{T}$ the trace of the energy-momentum tensor.

• The result shows that the action of $\Lambda$CDM is a combination of a linear term, a constant ($-2\Lambda$) and a non-linear term given by the product $\sqrt{-T}F_g\left[(T^{1/3}/16\pi G)\left(16\pi G\mathcal{T}+T+8\Lambda\right)\right]$, with $F_g$ being a generic function.
• We show that to maintain conservation of energy-momentum tensor should impose that $F_g[y]$ must be linear on the trace $\mathcal{T}$.
• This reconstruction decays in the $f(T)$ Theory for $F_g\equiv Q$, with $Q$ a constant.