Bouncing Universe for deformed non-minimally coupled inflation model

In this paper, we consider non-minimally coupled gravity model. We choose some suitable new variables and achieve the new Hamiltonian and Lagrangian which have harmonic oscillator form. The corresponding Lagrangian is deformed by non-commutative geometry. In order to have solution for the bouncing universe we specify the potential in the equation state. In that case we draw the equation of state in terms of time and show that the equation of state cross $-1$. Such bouncing behavior lead us to apply some conditions on $theta$ and $beta$ from non-commutative geometry. Here, also we can check the stability of system due to deformation of the non-minimally coupled to gravity model. In order to examine the stability of system we obtain the variation of pressure with respect to density energy. Also, we draw the variation of pressure with respect to energy density and show the condition of stability.