Squared Torsion f(T,T)$f(T,\mathcal {T})$ Gravity and Its Cosmological Implications

We present the coupling of torsion scalar T and trace energy-momentum tensor $\mathcal {T}$ , which produces new modified f ( ) $f(T,\mathcal {T})$ gravity. Moreover, we consider functional form = α + β 2 {T}) =\alpha \mathcal {T}+\beta T^2$ where are free parameters. As an alternative to a cosmological constant, theory may offer theoretical explanation late-time acceleration. The recent observational data considered model especially bounds on parameters is applied in detail. Furthermore, analyze behavior deceleration, effective equation state total However, it seen that deceleration parameter depicts transition from acceleration dark sector shows quintessence-like evolution.