Palatini Formulation of Modified Gravity with $\ln R$ Terms

TL;DR

This paper explores the Palatini formulation of a modified gravity theory with a logarithmic R term, showing it can explain cosmic acceleration and discussing its scalar-tensor equivalence and experimental constraints.

Contribution

It demonstrates that Palatini $ ext{ln} R$ gravity can produce accelerated expansion and analyzes its scalar-tensor form and experimental viability.

Findings

$ ext{ln} R$ gravity drives exponential cosmic acceleration

Reduces to standard Friedmann evolution at high redshift

Potential conflict with electron-electron scattering experiments

Abstract

Recently, corrections to the standard Einstein-Hilbert action are proposed to explain the current cosmic acceleration in stead of introducing dark energy. We discuss the Palatini formulation of the modified gravity with a $\ln R$ term suggested by Nojiri and Odintsov. We show that in the Palatini formulation, the $\ln R$ 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 $\ln R$ gravity may still have a conflict with electron-electron scattering experiment which stimulates us to pursue a more fundamental theory which can give the $\ln R$ gravity as an effective theory. Finally, we discuss a problem faced with the extension of the $\ln R$ gravity by adding $R^m$ terms.