  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.
