Newtonian limit of the singular f(R) gravity in the Palatini formalism

TL;DR

This paper investigates the Newtonian limit of certain f(R) gravity theories in the Palatini formalism, showing that models with specific singularities do not recover Newtonian gravity, challenging their viability for explaining cosmological acceleration.

Contribution

It demonstrates that f(R) models with poles at R=0 in the Palatini formalism lack a proper Newtonian limit, providing a critical assessment of their physical viability.

Findings

Models with poles of order n in R=0 do not have a good Newtonian limit.

The specific model with 1/R terms fails to reproduce Newtonian gravity.

Certain singular f(R) theories are incompatible with classical limits.

Abstract

Recently D. Vollick [Phys. Rev. D68, 063510 (2003)] has shown that the inclusion of the 1/R curvature terms in the gravitational action and the use of the Palatini formalism offer an alternative explanation for cosmological acceleration. In this work we show not only that this model of Vollick does not have a good Newtonian limit, but also that any f(R) theory with a pole of order n in R=0 and its second derivative respect to R evaluated at Ro is not zero, where Ro is the scalar curvature of background, does not have a good Newtonian limit.