1212.4781 (F. D. Albareti et al.)

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

F. D. Albareti, J. A. R. Cembranos, A. de la Cruz-Dombriz, A. Dobado

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.

View original: http://arxiv.org/abs/1212.4781