A new model of arcsin-gravity

The new model of modified $F(R)$ gravity theory with the function $F(R) = R+(a/\gamma) \arcsin(\gamma R)$ is suggested and investigated. Constant curvature solutions corresponding to the extremum of the effective potential are obtained. We consider both the Jordan and Einstein frames, and the potential and the mass of the scalar degree of freedom are found. It was shown that the de Sitter space-time is unstable but the flat space-time is stable. We calculate the slow-roll parameters $\epsilon$, $\eta$, and the $e$-fold number of the model. Critical points of autonomous equations for the de Sitter phase and the matter dominated epoch are obtained and learned.