In this paper, we consider an exponential form for f(R) modified gravity as $f(R)=\tfrac{1}{\alpha }({e}^{\alpha R}-1)$, where α is a parameter with the dimension of (length)2. The theory is consistent with local tests which give a bound on the value of this parameter: α ≤ 2 × 10−6. We investigate the static solution of this model corresponding to the Schwarzschild-de Sitter space. We also study the Jordan and Einstein frames of the model and obtain the scalar field potential related to the Einstein frame. In this respect, the mass of the scalar field is calculated as a function of Ricci curvature. Furthermore, by performing a dynamical system approach, we investigate the dimensionless parameters in the model and study the stability of the critical points in the phase space. Finally, we study the realization of inflation in this model and its graceful exit.
