Modified arctan-gravity model mimicking a cosmological constant

Understand

A novel theory of $F(R)$ gravity with the Lagrangian density ${\cal L}=[R-(b/\beta)\arctan\left(\beta R\right)]/(2\kappa^2)$ is analyzed.

• Constant curvature solutions of the model are found, and the potential of the scalar field and the mass of a scalar degree of freedom in Einstein's frame are derived.
• The cosmological parameters of the model are calculated, which are in agreement with the PLANCK data.
• Critical points for the de Sitter phase and the matter dominated epoch of autonomous equations are obtained and studied.