Logarithmic gravity model

The modified $F(R)$ gravity theory with the function $F(R)=-(1/\beta)\ln(1-\beta R)$ is studied. The action at small coupling $\beta$ becomes Einstein--Hilbert action. The bound on the parameter $\beta$ from local tests is $\beta\leq 2\times 10^{-6}$ cm$^2$. We find the constant curvature solutions and it was shown that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. The potential and the mass of the scalar field (scalaron) are obtained in the Einstein's frame. The slow-roll cosmological parameters are studied and e-folds number is evaluated. The critical points of autonomous equations are analyzed. The function $m(r)$ that describes the deviation from the $\Lambda$CDM model is calculated.