2009/06/30 by M. J. Reboucas, M. J. Rebouças, J. Santos · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.80.063009
published as Phys.Rev.D80:063009,2009 · 7 pages, V3: Version to appear in Phys. Rev. D (2009), typos corrected, the generality of our main results is emphasized. The illustrative character of a particular theory is also made explicit
arxiv created 2009/09/21 · openalex publication_date 2009/09/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The f(R) gravity theories provide an alternative way to explain the current cosmic acceleration without a dark energy matter component. If gravity is governed by a f(R) theory, a number of issues should be reexamined in this framework, including the violation of causality problem on nonlocal scale. We examine the question as to whether the f(R) gravity theories permit space-times in which the causality is violated. We show that the field equations of these f(R) gravity theories do not exclude solutions with breakdown of causality for a physically well-motivated perfect-fluid matter content. We demonstrate that every perfect-fluid G"odel-type solution of a generic f(R) gravity satisfying the condition df/dR>0 is necessarily isometric to the G"odel geometry, and therefore presents violation of causality. This result extends a theorem on G"odel-type models, which has been established in the context of general relativity. We also derive an expression for the critical radius rc (beyond which the causality is violated) for an arbitrary f(R) theory, making apparent that the violation of causality depends on both the f(R) gravity theory and the matter content. As an illustration, we concretely take a recent f(R) gravity theory that is free from singularities of the Ricci scalar and is cosmologically viable, and show that this theory accommodates noncausal as well as causal G"odel-type solutions.