A new $F(R)$-gravity model

We propose a new model of modified $F(R)$ gravity theory with the function $F(R) = (1/\beta) \arcsin(\beta R)$. Constant curvature solutions corresponding to the flat and de Sitter spacetime are obtained. The Jordan and Einstein frames are considered; the potential and the mass of the scalar degree of freedom are found. We show that the flat spacetime is stable and the de Sitter spacetime is unstable. The slow-roll parameters $\epsilon$, $\eta$, and the $e$-fold number of the model are evaluated in the Einstein frame. The index of the scalar spectrum power-law $n_s$ and the tensor-to-scalar ratio $r$ are calculated. Critical points of autonomous equations for the de Sitter phase and the matter dominated epoch are found and studied. We obtain the approximate solution of equations of motion which is the deviation from the de Sitter phase in the Jordan frame. It is demonstrated that the model passes the matter stability test.