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

Abstract

In General Relativity without a cosmological constanta non-positive contribution from the space-time geometry to Raychaudhuri equation is found provided that particular energy conditionsare 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 positivecontribution to Raychaudhuri equation from space-time geometry should occur since this is the case in an accelerated expandingRobertson-Walker model for congruences followed by fundamental observers. Modified gravity theories provide the possibilityof 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 theparameter 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.