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

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2013

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Iop Publishing Ltd
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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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©2013 IOP Publishing Ltd and Sissa Medialab srl This work has been supported by MINECO (Spain) project numbers FIS2011-23000, FPA2011-27853-C02-01 and Consolider-Ingenio MULTIDARK CSD2009-00064. AdlCD also acknowledges financial support from Marie Curie - Beatriu de Pinós contract BP-B00195, Generalitat de Catalunya and ACGC, University of Cape Town.

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