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.