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arXiv · 1212.4781

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

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

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F. D. Albareti, J. A. R. Cembranos, A. de la Cruz-Dombriz, A. Dobado. 2013-07-09. On the non-attractive character of gravity in f(R) theories. https://doi.org/10.1088/1475-7516%2F2013%2F07%2F009

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