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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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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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