Local Gravity Constraints and Power Law f(R) Theories

TL;DR

This paper explores how power law f(R) gravity theories relate to scalar fields with exponential potentials, using the chameleon mechanism to test their compatibility with Solar System constraints, and finds they may be indistinguishable from Einstein gravity.

Contribution

It demonstrates the application of the chameleon mechanism to constrain power law f(R) theories, showing their potential indistinguishability from Einstein gravity in Solar System tests.

Findings

Power law f(R) theories can be conformally mapped to scalar fields with exponential potentials.

Chameleon mechanism constrains the scalar field's potential to match Solar System experiments.

Power law f(R) models may be indistinguishable from Einstein-Hilbert gravity in observational tests.

Abstract

There is a conformal equivalence between power law $f(R)$ theories and scalar field theories in which the scalar degree of freedom evolves under the action of an exponential potential function. In the scalar field representation there is a strong coupling of the scalar field with the matter sector due to the conformal transformation. We use chameleon mechanism to implement constraints on the potential function of the scalar field in order that the resulting model be in accord with Solar System experiments. Investigation of these constraints reveals that there may be no possibility to distinguish between a power law $f(R)$ function and the usual Einstein-Hilbert Lagrangian density.