Weak-field limit of f(R)-gravity in three and more spatial dimensions

TL;DR

This paper analyzes the weak-field behavior of f(R) gravity theories in multiple spatial dimensions, showing that only in three dimensions do the models align with experimental data, with implications for constraining f(R) parameters.

Contribution

It extends the analysis of f(R) gravity to arbitrary dimensions, demonstrating that agreement with experiments occurs only in three-dimensional space, and generalizes results to perfect fluid sources.

Findings

Agreement with experimental data only in D=3

Extra dimensions require toroidal compactification

Formulas useful for constraining f(R) models

Abstract

We investigate a point-like massive source in non-linear f(R) theories in the case of arbitrary number of spatial dimensions D\geq 3. If D>3 then extra dimensions undergo toroidal compactification. We consider a weak-field approximation with Minkowski and de Sitter background solutions. In both these cases point-like massive sources demonstrate good agreement with experimental data only in the case of ordinary three-dimensional (D=3) space. We generalize this result to the case of perfect fluid with dust-like equations of state in the external and internal spaces. This perfect fluid is uniformly smeared over all extra dimensions and enclosed in a three-dimensional sphere. In ordinary three dimensional (D=3) space, our formulas are useful for experimental constraints on parameters of f(R) models.