Solar system tests do not rule out 1/R gravity

TL;DR

This paper argues that Solar system tests do not exclude 1/R gravity modifications because the boundary conditions and equations of motion in such theories are different from standard gravity, allowing consistent solutions.

Contribution

It clarifies the role of boundary conditions in 1/R gravity and shows that previous assumptions about smoothness of the Ricci scalar are incorrect, preserving the viability of 1/R gravity.

Findings

Boundary conditions in 1/R gravity differ from standard gravity.

Proper boundary conditions allow 1/R gravity to pass Solar system tests.

Previous assumptions about Ricci scalar smoothness are invalid.

Abstract

We argue that Solar system tests do not rule out 1/R gravity at least due to the reason addressed in Phys. Rev. D 74 (2006) 121501 [astro-ph/0610483] (ref. [1]) and subsequent published papers. Ref. [1] has not only modified the Einstein-Hilbert action but also has changed the boundary conditions since they altered the equations of motion. In Einstein-Hilbert action equations are second order, so the fall off of the fields suffices to single out a unique solution. In 1/R gravity the equations are fourth order, so we should impose additional boundary conditions. Perhaps the boundary condition we must impose is that the abrupt change in the second derivative of the metric near the surface of the Sun remains intact by adding `1/R' corrections to the equations of motion. The solution of 1/R gravity with this boundary condition remains consistent with the solar system tests. Ref. [1] assumes that as soon as they perturbatively modified the equations then the Ricci scalar becomes smooth on the surface of the Sun. This assumption is simply wrong because the boundary conditions and equations of motions are two different entities.