Strong energy condition and the repulsive character of f(R) gravity
  The Raychaudhuri equation enables to examine the whole spacetime structure without specific solutions of Einstein's equations, playing a central role for the understanding of the gravitational interaction in Cosmology. In General Relativity, without considering a cosmological constant, a non-positive contribution in the Raychaudhuri equation is usually interpreted as the manifestation of the attractive character of gravity. In this case, particular energy conditions -- indeed the strong energy condition -- must be assumed in order to guarantee the attractive character. In the context of f(R) gravity, however, even assuming the standard energy conditions one may have a positive contribution to the Raychaudhuri equation. Besides providing a simple way to explain the observed cosmic acceleration, this fact opens the possibility of a repulsive character of this kind of gravity. In order to discuss physical bounds on f(R) models, we address the attractive/non-attractive character of f(R) gravity considering the Raychaudhuri equation and assuming the strong energy condition along with recent estimates of the cosmographic parameters. 
Crislane S. Santos, Janilo Santos, Salvatore Capozziello and Jailson   S. Alcaniz
gr-qc astro-ph.CO