Notes on Born-Infeld-like modified gravity

Understand

We investigate the modified $F(R)$ gravity theory with the function $F(R) = (1-\sqrt{1-2\lambda R-\sigma (\lambda R)^2})/\lambda$.

• The action is converted into Einstein$-$Hilbert action at small values of $\lambda$ and $\sigma$.
• The local tests give a bound on the parameters, $\lambda(1+\sigma)\leq 2\times 10^{-6}$ cm$^2$.
• The Jordan and Einstein frames are considered, the potential, and the mass of the scalar field were obtained.