On the non-attractive character of gravity in f(R) theories

TL;DR

This paper investigates the potential for f(R) gravity theories to produce a positive contribution to the Raychaudhuri equation, challenging the traditional view of gravity's always attractive nature in General Relativity.

Contribution

It derives explicit upper bounds for geometric contributions in f(R) theories and analyzes parameter constraints to allow for a non-attractive, possibly repulsive, gravitational effect.

Findings

Explicit upper bounds for geometric contributions in f(R) models.

Parameter constraints for positive contributions in specific f(R) models.

Implications for the equivalent Brans-Dicke formulation.

Abstract

In General Relativity without a cosmological constant a non-positive contribution from the space-time geometry to Raychaudhuri equation is found provided that particular energy conditions are assumed and regardless the considered solution of the Einstein's equations. This fact is usually interpreted as a manifestation of the attractive character of gravity. Nevertheless, a positive contribution to Raychaudhuri equation from space-time geometry should occur since this is the case in an accelerated expanding Robertson-Walker model for congruences followed by fundamental observers. Modified gravity theories provide the possibility of a positive contribution although the standard energy conditions are assumed. We address this important issue in the context of f(R) theories, deriving explicit upper bounds for the contribution of space-time geometry to the Raychaudhuri equation. Then, we examine the parameter constraints for some paradigmatic f(R) models in order to ensure a positive contribution to this equation. Furthermore, we consider the implications of these upper bounds in the equivalent formulation of f(R) theories as a Brans-Dicke model.