Modified Gravity with ln R Terms and Cosmic Acceleration

The modified gravity with ln R or R^–n (ln R)^m terms which grow at small curvature is discussed. It is shown that such a model which has a well-defined Newtonian limit may eliminate the need for dark energy and may provide the current cosmic acceleration. It is demonstrated that R² terms are important not only for early time inflation but also to avoid the instabilities and the linear growth of the gravitational force. It is very interesting that the condition of no linear growth for gravitational force coincides with the one for scalar mass in the equivalent scalar-tensor theory to be very large. Thus, modified gravity with R² term seems to be a viable classical theory.