Noether symmetry in teleparalle extended gravity ‎

In this paper, we study the  modified gravity theory, where  and  represent the scalar-torsion and trace of energy-momentum tensor, respectively. According to our cosmological study, we show that the  gravity theory has a good agreement with observations. Function type for  can be determined by several factors. The most important motivation for determining  is that the Lagrangian of model follows the Noether continues symmetry; therefore, according to the Noether approach, we try to determine the function of . Moreover, the proposed model should behave in agreement with observations in terms of phenomenology. As a result, we compared the predictions of the model with observation constrains, for example, the cosmic microwave background and Hubble diagram can be mentioned. In this paper, we study the  gravity in the FRW space-time. So, we achieved the effective Lagrangian with respect to independent variables, scale factor , scalar-torsion  and trace of energy-momentum tensor . After imposing the Noether symmetry to Lagrangian, we can introduce the suitable form for the function. . Then, we calculated the Noether conservative quantity for the model.