Mimicking general relativity in the solar system

TL;DR

This paper demonstrates that certain second-order Brans-Dicke theories with Gauss-Bonnet corrections can closely mimic general relativity in the solar system, passing local gravity tests while remaining viable for cosmological dark energy models.

Contribution

It constructs a generic second-order Brans-Dicke theory with Gauss-Bonnet terms that interpolates between GR and BD gravity, ensuring compatibility with local experiments.

Findings

The theory can produce Eddington parameters arbitrarily close to 1.

The solutions are stable against small timelike perturbations.

The model passes stringent local gravity constraints.

Abstract

In order for a modified gravity model to be a candidate for cosmological dark energy it has to pass stringent local gravity experiments. We find that a Brans-Dicke (BD) theory with well-defined second order corrections that include the Gauss-Bonnet term possess this feature. We construct the generic second order theory that gives, to linear order, a BD metric solution for a point-like mass source. We find that these theories interpolate between general relativity (GR) and BD gravity. In particular it is found that the relevant Eddington parameter, that is commonly heavily constrained by time delay experiments, can be arbitrarily close to the GR value of 1, with an arbitrary BD parameter. We find the region where the solution is stable to small timelike perturbations.