Makarenko, A. N., Odintsov, S. D., & Olmo, G. J. (2014). Little Rip, Lambda CDM and singular dark energy cosmology from Born-Infeld-f(R) gravity. Phys. Lett. B, 734, 36–40.
Abstract: We study late-time cosmic accelerating dynamics from Born-Infeld-f(R) gravity in a simplified conformal approach. We find that a variety of cosmic effects such as Little Rip, Lambda CDM universe and dark energy cosmology with finite time future singularities may occur. Unlike the convenient Born-Infeld gravity where in the absence of matter only de Sitter expansion may emerge, apparently any FRW cosmology may be reconstructed from this conformal version of the Born-Infeld-f(R) theory. Despite the fact that the explicit form of f(R) is fixed by the conformal ansatz, the relation between the two metrics in this approach may be changed so as to bring out any desired FRW cosmology.
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Bazeia, D., Losano, L., Olmo, G. J., & Rubiera-Garcia, D. (2014). Black holes in five-dimensional Palatini f(R) gravity and implications for the AdS/CFT correspondence. Phys. Rev. D, 90(4), 044011–8pp.
Abstract: We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric and affine structures of space-time is made (the Palatini approach). We illustrate this fact by considering the case of Palatini f(R) gravities in five dimensions. Our results provide an alternative avenue to explore new domains of the AdS/CFT correspondence without resorting to ad hoc quasitopological constructions.
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Odintsov, S. D., Olmo, G. J., & Rubiera-Garcia, D. (2014). Born-Infeld gravity and its functional extensions. Phys. Rev. D, 90(4), 044003–8pp.
Abstract: We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the connection and an Einstein-like representation for the metric field equations of this family of theories. For particular cases we consider applications to the early-time cosmology and find that nonsingular universes with a cosmic bounce are very generic and robust solutions.
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Makarenko, A. N., Odintsov, S., & Olmo, G. J. (2014). Born-Infeld f(R) gravity. Phys. Rev. D, 90(2), 024066–15pp.
Abstract: Motivated by the properties of matter quantum fields in curved space-times, we work out a gravity theory that combines the Born-Infeld gravity Lagrangian with an f(R) piece. To avoid ghostlike instabilities, the theory is formulated within the Palatini approach. This construction provides more freedom to address a number of important questions, such as the dynamics of the early Universe and the cosmic accelerated expansion, among others. In particular, we consider the effect that adding an f(R) = aR(2) term has on the early-time cosmology. We find that bouncing solutions are robust against these modifications of the Lagrangian whereas the solutions with loitering behavior of the original Born-Infeld theory are very sensitive to the R-2 term. In fact, these solutions are modified in such a way that a plateau in the H-2 function may arise, yielding a period of (approximately) de Sitter inflationary expansion. This inflationary behavior may be found even in a radiation-dominated universe.
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Lobo, F. S. N., Martinez-Asencio, J., Olmo, G. J., & Rubiera-Garcia, D. (2014). Dynamical generation of wormholes with charged fluids in quadratic Palatini gravity. Phys. Rev. D, 90(2), 024033–15pp.
Abstract: The dynamical generation of wormholes within an extension of General Relativity (GR) containing (Planck's scale-suppressed) Ricci-squared terms is considered. The theory is formulated assuming the metric and connection to be independent (Palatini formalism) and is probed using a charged null fluid as a matter source. This has the following effect: starting from Minkowski space, when the flux is active the metric becomes a charged Vaidya-type one, and once the flux is switched off the metric settles down into a static configuration such that far from the Planck scale the geometry is virtually indistinguishable from that of the standard Reissner-Nordstrom solution of GR. However, the innermost region undergoes significant changes, as the GR singularity is generically replaced by a wormhole structure. Such a structure becomes completely regular for a certain charge-to-mass ratio. Moreover, the nontrivial topology of the wormhole allows us to define a charge in terms of lines of force trapped in the topology such that the density of lines flowing across the wormhole throat becomes a universal constant. In light of our results, we comment on the physical significance of curvature divergences in this theory and the topology change issue, which support the view that space-time could have a foamlike microstructure pervaded by wormholes generated by quantum gravitational effects.
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