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Olmo, G. J., & Sanchis-Alepuz, H. (2011). Hamiltonian formulation of Palatini f(R) theories a la Brans-Dicke theory. Phys. Rev. D, 83(10), 104036–11pp.
Abstract: We study the Hamiltonian formulation of f(R) theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a nontrivial potential. The Palatini case, which corresponds to the omega = -3/2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is nondynamical. We derive, compare, and discuss the constraints and evolution equations for the omega = -3/2 and omega not equal -3/2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the omega = -3/2 case is well formulated and there is no reason to believe that it is not well posed in general.
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Agullo, I., Navarro-Salas, J., Olmo, G. J., & Parker, L. (2011). Remarks on the renormalization of primordial cosmological perturbations. Phys. Rev. D, 84(10), 107304–5pp.
Abstract: We briefly review the need to perform renormalization of inflationary perturbations to properly work out the physical power spectra. We also summarize the basis of (momentum-space) renormalization in curved spacetime and address several misconceptions found in recent literature on this subject.
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Olmo, G. J., & Rubiera-Garcia, D. (2011). Palatini f(R) black holes in nonlinear electrodynamics. Phys. Rev. D, 84(12), 124059–14pp.
Abstract: The electrically charged Born-Infeld black holes in the Palatini formalism for f(R) theories are analyzed. Specifically we study those supported by a theory f(R) = R +/- R(2)/R(P), where R(P) is Planck's curvature. These black holes only differ from their General Relativity counterparts very close to the center but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model f(R) = R – R(2)/R(P) the singularity is shifted to a finite radius, r(+), and the Kretschmann scalar diverges only as 1/(r-r(+))(2).
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Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2012). Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration. Phys. Rev. D, 85(8), 084016–5pp.
Abstract: We present a novel approach to modified theories of gravity which consists of adding to the Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we show that the theory can pass the Solar System observational constraints even if the scalar field is very light. This implies the existence of a long-range scalar field, which is able to modify the cosmological and galactic dynamics but leaves the Solar System unaffected. We also verify the absence of instabilities in perturbations and provide explicit models which are consistent with local tests and lead to the late-time cosmic acceleration.
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Olmo, G. J., & Rubiera-Garcia, D. (2012). Reissner-Nordstrom black holes in extended Palatini theories. Phys. Rev. D, 86(4), 044014–15pp.
Abstract: We study static, spherically symmetric solutions with an electric field in an extension of general relativity containing a Ricci-squared term and formulated in the Palatini formalism. We find that all the solutions present a central core whose area is proportional to the Planck area times the number of charges. Far from the core, curvature invariants quickly tend to those of the usual Reissner-Nordstrom solution, though the structure of horizons may be different. In fact, besides the structures found in the Reissner-Nordstrom solution of general relativity, we find black hole solutions with just one nondegenerate horizon (Schwarzschild-like) and nonsingular black holes and naked cores. The charge-to-mass ratio of the nonsingular solutions implies that the core matter density is independent of the specific amounts of charge and mass and of order the Planck density. We discuss the physical implications of these results for astrophysical and microscopic black holes, construct the Penrose diagrams of some illustrative cases, and show that the maximal analytical extension of the nonsingular solutions implies a bounce of the radial coordinate.
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