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Maluf, R. V., & Olmo, G. J. (2023). Vacuum polarization and induced Maxwell and Kalb-Ramond effective action in very special relativity. Phys. Rev. D, 108(9), 095022–13pp.
Abstract: This work investigates the implications of very special relativity (VSR) on the calculation of vacuum polarization for fermions in the presence of Maxwell and Kalb-Ramond gauge fields in four-dimensional spacetime. We derive the SIM(2)-covariant gauge theory associated with an Abelian antisymmetric twotensor and its corresponding field strength. We demonstrate that the free VSR-Kalb-Ramond electrodynamics is equivalent to a massive scalar field with a single polarization. Furthermore, we determine an explicit expression for the effective action involving Maxwell and Kalb-Ramond fields due to fermionic vacuum polarization at one-loop order. The quantum corrections generate divergences free of nonlocal terms only in the VSR-Maxwell sector. At the same time, we observe UV/IR mixing divergences due to the entanglement of VSR-nonlocal effects with quantum higher-derivative terms for the Kalb-Ramond field. However, in the lower energy limit, the effective action can be renormalized like in the Lorentz invariant case.
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Maluf, R. V., Mora-Perez, G., Olmo, G. J., & Rubiera-Garcia, D. (2024). Nonsingular, Lump-like, Scalar Compact Objects in (2+1)-Dimensional Einstein Gravity. Universe, 10(6), 258–13pp.
Abstract: We study the space-time geometry generated by coupling a free scalar field with a noncanonical kinetic term to general relativity in (2+1) dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions in static and circularly symmetric scenarios, we classify the various types of solutions and focus on a branch that yields asymptotically flat geometries. We show that the solutions within such a branch can be divided in two types, namely naked singularities and nonsingular objects without a center. In the latter, the energy density is localized around a maximum and vanishes only at infinity and at an inner boundary. This boundary has vanishing curvatures and cannot be reached by any time-like or null geodesic in finite affine time. This allows us to consistently interpret such solutions as nonsingular, lump-like, static compact scalar objects whose eventual extension to the (3+1)-dimensional context could provide structures of astrophysical interest.
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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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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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Magalhaes, R. B., Ribeiro, G. P., Lima, H. C. D. J., Olmo, G. J., & Crispino, L. C. B. (2024). Singular space-times with bounded algebraic curvature scalars. J. Cosmol. Astropart. Phys., 05(5), 114–34pp.
Abstract: We show that the absence of unbounded algebraic curvature invariants constructed from polynomials of the Riemann tensor cannot guarantee the absence of strong singularities. As a consequence, it is not sufficient to rely solely on the analysis of such scalars to assess the regularity of a given space-time. This conclusion follows from the analysis of incomplete geodesics within the internal region of asymmetric wormholes supported by scalar matter which arise in two distinct metric-affine gravity theories. These wormholes have bounded algebraic curvature scalars everywhere, which highlights that their finiteness does not prevent the emergence of pathologies (singularities) in the geodesic structure of space-time. By analyzing the tidal forces in the internal wormhole region, we find that the angular components are unbounded along incomplete radial time-like geodesics. The strength of the singularity is determined by the evolution of Jacobi fields along such geodesics, finding that it is of strong type, as volume elements are torn apart as the singularity is approached. Lastly, and for completeness, we consider the wormhole of the quadratic Palatini theory and present an analysis of the tidal forces in the entire space-time.
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