Palatini formulation of modified gravity with lnR terms

Recently, corrections to the standard Einstein-Hilbert action are proposed to explain the current cosmic acceleration instead of introducing dark energy. We discuss the Palatini formulation of the modified gravity with a lnR term suggested by Nojiri and Odintsov. We show that in the Palatini formulation, the lnR gravity can drive a current exponential accelerated expansion and it reduces to the standard Friedmann evolution for high redshift region. We also discuss the equivalent scalar-tensor formulation of the theory. We indicate that the lnR gravity may still have a conflict with electron-electron scattering experiment which stimulates us to pursue a more fundamental theory which can give the lnR gravity as an effective theory. Finally, we discuss a problem faced with the extension of the lnR gravity by adding Rm terms