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Benisty, D., Olmo, G. J., & Rubiera-Garcia, D. (2021). Singularity-Free and Cosmologically Viable Born-Infeld Gravity with Scalar Matter. Symmetry-Basel, 13(11), 2108–24pp.
Abstract: The early cosmology, driven by a single scalar field, both massless and massive, in the context of Eddington-inspired Born-Infeld gravity, is explored. We show the existence of nonsingular solutions of bouncing and loitering type (depending on the sign of the gravitational theory's parameter, epsilon) replacing the Big Bang singularity, and discuss their properties. In addition, in the massive case, we find some new features of the cosmological evolution depending on the value of the mass parameter, including asymmetries in the expansion/contraction phases, or a continuous transition between a contracting phase to an expanding one via an intermediate loitering phase. We also provide a combined analysis of cosmic chronometers, standard candles, BAO, and CMB data to constrain the model, finding that for roughly |epsilon|& LSIM;5 & BULL;10-8m2 the model is compatible with the latest observations while successfully removing the Big Bang singularity. This bound is several orders of magnitude stronger than the most stringent constraints currently available in the literature.
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Beltran Jimenez, J., Heisenberg, L., Olmo, G. J., & Rubiera-Garcia, D. (2018). Born-Infeld inspired modifications of gravity. Phys. Rep., 727, 1–129.
Abstract: General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordinary ability to regularise the gravitational dynamics, leading to non-singular cosmologies and regular black hole spacetimes in a very robust manner and without resorting to quantum gravity effects. This has boosted the interest in these theories in applications to stellar structure, compact objects, inflationary scenarios, cosmological singularities, and black hole and wormhole physics, among others. We review the motivations, various formulations, and main results achieved within these theories, including their observational viability, and provide an overview of current open problems and future research opportunities.
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Olmo, G. J., Rubiera-Garcia, D., & Wojnar, A. (2020). Stellar structure models in modified theories of gravity: Lessons and challenges. Phys. Rep., 876, 1–75.
Abstract: The understanding of stellar structure represents the crossroads of our theories of the nuclear force and the gravitational interaction under the most extreme conditions observably accessible. It provides a powerful probe of the strong field regime of General Relativity, and opens fruitful avenues for the exploration of new gravitational physics. The latter can be captured via modified theories of gravity, which modify the Einstein-Hilbert action of General Relativity and/or some of its principles. These theories typically change the Tolman-Oppenheimer-Volkoff equations of stellar's hydrostatic equilibrium, thus having a large impact on the astrophysical properties of the corresponding stars and opening a new window to constrain these theories with present and future observations of different types of stars. For relativistic stars, such as neutron stars, the uncertainty on the equation of state of matter at supranuclear densities intertwines with the new parameters coming from the modified gravity side, providing a whole new phenomenology for the typical predictions of stellar structure models, such as mass-radius relations, maximum masses, or moment of inertia. For non-relativistic stars, such as white, brown and red dwarfs, the weakening/strengthening of the gravitational force inside astrophysical bodies via the modified Newtonian (Poisson) equation may induce changes on the star's mass, radius, central density or luminosity, having an impact, for instance, in the Chandrasekhar's limit for white dwarfs, or in the minimum mass for stable hydrogen burning in high-mass brown dwarfs. This work aims to provide a broad overview of the main such results achieved in the recent literature for many such modified theories of gravity, by combining the results and constraints obtained from the analysis of relativistic and non-relativistic stars in different scenarios. Moreover, we will build a bridge between the efforts of the community working on different theories, formulations, types of stars, theoretical modelings, and observational aspects, highlighting some of the most promising opportunities in the field.
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Guendelman, E. I., Olmo, G. J., Rubiera-Garcia, D., & Vasihoun, M. (2013). Nonsingular electrovacuum solutions with dynamically generated cosmological constant. Phys. Lett. B, 726(4-5), 870–875.
Abstract: We consider static spherically symmetric configurations in a Palatini extension of General Relativity including R-2 and Ricci-squared terms, which is known to replace the central singularity by a wormhole in the electrovacuum case. We modify the matter sector of the theory by adding to the usual Maxwell term a nonlinear electromagnetic extension which is known to implement a confinement mechanism in flat space. One feature of the resulting theory is that the nonlinear electric field leads to a dynamically generated cosmological constant. We show that with this matter source the solutions of the model are asymptotically de Sitter and possess a wormhole topology. We discuss in some detail the conditions that guarantee the absence of singularities and of traversable wormholes.
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Lobo, F. S. N., Martinez-Asencio, J., Olmo, G. J., & Rubiera-Garcia, D. (2014). Planck scale physics and topology change through an exactly solvable model. Phys. Lett. B, 731, 163–167.
Abstract: We consider the collapse of a charged radiation fluid in a Planck-suppressed quadratic extension of General Relativity (GR) formulated A la Palatini. We obtain exact analytical solutions that extend the charged Vaidya-type solution of GR, which allows to explore in detail new physics at the Planck scale. Starting from Minkowski space, we find that the collapsing fluid generates wormholes supported by the electric field. We discuss the relevance of our findings in relation to the quantum foam structure of space-time and the meaning of curvature divergences in this theory.
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Olmo, G. J., & Rubiera-Garcia, D. (2015). Brane-world and loop cosmology from a gravity-matter coupling perspective. Phys. Lett. B, 740, 73–79.
Abstract: We show that the effective brane-world and the loop quantum cosmology background expansion histories can be reproduced from a modified gravity perspective in terms of an f (R) gravity action plus a g(R) term non-minimally coupled with the matter Lagrangian. The reconstruction algorithm that we provide depends on a free function of the matter density that must be specified in each case and allows to obtain analytical solutions always. In the simplest cases, the function f (R) is quadratic in the Ricci scalar, R, whereas g(R) is linear. Our approach is compared with recent results in the literature. We show that working in the Palatini formalism there is no need to impose any constraint that keeps the equations second order, which is a key requirement for the successful implementation of the reconstruction algorithm.
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Bejarano, C., Delhom, A., Jimenez-Cano, A., Olmo, G. J., & Rubiera-Garcia, D. (2020). Geometric inequivalence of metric and Palatini formulations of General Relativity. Phys. Lett. B, 802, 135275–4pp.
Abstract: Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K (R beta μnu R alpha beta μnu)-R-alpha, can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the connection.
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Olmo, G. J., Rubiera-Garcia, D., & Saez-Chillon Gomez, D. (2022). New light rings from multiple critical curves as observational signatures of black hole mimickers. Phys. Lett. B, 829, 137045–5pp.
Abstract: We argue that the appearance of additional light rings in a shadow observation – beyond the infinite sequence of exponentially demagnified self-similar rings foreseen in the Kerr solution – would make a compelling case for the existence of black hole mimickers having multiple critical curves. We support this claim by discussing three different scenarios of spherically symmetric wormhole geometries having two such critical curves, and explicitly work out the optical appearance of one such object when surrounded by an optically and geometrically thin accretion disk.
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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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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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