Beltran Jimenez, J., Heisenberg, L., & Olmo, G. J. (2014). Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-lnfeld. J. Cosmol. Astropart. Phys., 11(11), 004–26pp.
Abstract: We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a minimal version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. In vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.
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Beltran Jimenez, J., Heisenberg, L., & Olmo, G. J. (2015). Tensor perturbations in a general class of Palatini theories. J. Cosmol. Astropart. Phys., 06(6), 026–16pp.
Abstract: We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the spacetime metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.
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Beltran Jimenez, J., Heisenberg, L., Olmo, G. J., & Ringeval, C. (2015). Cascading dust inflation in Born-lnfeld gravity. J. Cosmol. Astropart. Phys., 11(11), 046–30pp.
Abstract: In the framework of Born-Infeld inspired gravity theories, which deviates from General Relativity (GR) in the high curvature regime, we discuss the viability of Cosmic Inflation without scalar fields. For energy densities higher than the new mass scale of the theory, a gravitating (lust component is shown to generically induce an accelerated expansion of the Universe. Within such a simple scenario, inflation gracefiffly exits when the CR regime is recovered, but the Universe would remain matter dominated. In order to implement a reheating era after inflation, we then consider inflation to be driven by a mixture of unstable dust species decaying into radiation. Because the speed of sound gravitates within the BornInfeld model under consideration, our scenario ends up being predictive on various open questions of the inflationary paradigm. The total number of e-folds of acceleration is given by the lifetime of the unstable dust components and is related to the duration of reheating. As a result, inflation does not last much longer than the number of e-folds of deceleration allowing a small spatial curvature and large scale deviations to isotropy to be observable today. Energy densities are self-regulated as inflation can only start for a total energy density less than a threshold value, again related to the species' lifetime. Above this threshold, the Universe may bc nee thereby avoiding a singularity. Another distinctive feature is that the accelerated expansion is of the superinflationary ldnd, namely the first Hubble flow function is negative. We show however that the tensor modes are never excited and the tensor-to-scalar ratio is always vanishing, independently of the energy scale of inflation.
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Afonso, V. I., Olmo, G. J., & Rubiera-Garcia, D. (2017). Scalar geons in Born-Infeld gravity. J. Cosmol. Astropart. Phys., 08(8), 031–35pp.
Abstract: The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r = 2 M, while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.
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Beltran Jimenez, J., Heisenberg, L., Olmo, G. J., & Rubiera-Garcia, D. (2017). On gravitational waves in Born-Infeld inspired non-singular cosmologies. J. Cosmol. Astropart. Phys., 10(10), 029–23pp.
Abstract: We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.
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Afonso, V. I., Olmo, G. J., Orazi, E., & Rubiera-Garcia, D. (2019). New scalar compact objects in Ricci-based gravity theories. J. Cosmol. Astropart. Phys., 12(12), 044–20pp.
Abstract: Taking advantage of a previously developed method, which allows to map solutions of General Relativity into a broad family of theories of gravity based on the Ricci tensor (Ricci-based gravities), we find new exact analytical scalar field solutions by mapping the free-field static, spherically symmetric solution of General Relativity (GR) into quadratic f(R) gravity and the Eddington-inspired Born-Infeld gravity. The obtained solutions have some distinctive feature below the would-be Schwarzschild radius of a configuration with the same mass, though in this case no horizon is present. The compact objects found include wormholes, compact balls, shells of energy with no interior, and a new kind of object which acts as a kind of wormhole membrane. The latter object has Euclidean topology but connects antipodal points of its surface by transferring particles and null rays across its interior in virtually zero affine time. We point out the relevance of these results regarding the existence of compact scalar field objects beyond General Relativity that may effectively act as black hole mimickers.
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Guerrero, M., Mora-Perez, G., Olmo, G. J., Orazi, E., & Rubiera-Garcia, D. (2020). Rotating black holes in Eddington-inspired Born-Infeld gravity: an exact solution. J. Cosmol. Astropart. Phys., 07(7), 058–31pp.
Abstract: We find an exact, rotating charged black hole solution within Eddington-inspired Born-Infeld gravity. To this end we employ a recently developed correspondence or mapping between modified gravity models built as scalars out of contractions of the metric with the Ricci tensor, and formulated in metric-affine spaces (Ricci-Based Gravity theories) and General Relativity. This way, starting from the Kerr-Newman solution, we show that this mapping bring us the axisymmetric solutions of Eddington-inspired Born-Infeld gravity coupled to a certain model of non-linear electrodynamics. We discuss the most relevant physical features of the solutions obtained this way, both in the spherically symmetric limit and in the fully rotating regime. Moreover, we further elaborate on the potential impact of this important technical progress for bringing closer the predictions of modified gravity with the astrophysical observations of compact objects and gravitational wave astronomy.
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Guerrero, M., Olmo, G. J., & Rubiera-Garcia, D. (2021). Double shadows of reflection-asymmetric wormholes supported by positive energy thin-shells. J. Cosmol. Astropart. Phys., 04(4), 066–26pp.
Abstract: We consider reflection-asymmetric thin-shell wormholes within Palatini f(R) gravity using a matching procedure of two patches of electrovacuum space-times at a hypersurface (the shell) via suitable junction conditions. The conditions for having (linearly) stable wormholes supported by positive-energy matter sources are determined. We also identify some subsets of parameters able to locate the shell radius above the event horizon (when present) but below the photon sphere (on both sides). We illustrate with an specific example that such two photon spheres allow an observer on one of the sides of the wormhole to see another (circular) shadow in addition to the one generated by its own photon sphere, which is due to the photons passing above the maximum of the effective potential on its side and bouncing back across the throat due to a higher effective potential on the other side. We finally comment on the capability of these double shadows to seek for traces of new gravitational physics beyond that described by General Relativity.
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Guerrero, M., Olmo, G. J., Rubiera-Garcia, D., & Saez-Chillon Gomez, D. (2021). Shadows and optical appearance of black bounces illuminated by a thin accretion disk. J. Cosmol. Astropart. Phys., 08(8), 036–19pp.
Abstract: We study the light rings and shadows of an uniparametric family of spherically symmetric geometries interpolating between the Schwarzschild solution, a regular black hole, and a traversable wormhole, and dubbed as black bounces, all of them sharing the same critical impact parameter. We consider the ray-tracing method in order to study the impact parameter regions corresponding to the direct, lensed, and photon ring emissions, finding a broadening of all these regions for black bounce solutions as compared to the Schwarzschild one. Using this, we determine the optical appearance of black bounces when illuminated by three standard toy models of optically and geometrically thin accretion disks viewed in face-on orientation.
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Guerrero, M., Mora-Perez, G., Olmo, G. J., Orazi, E., & Rubiera-Garcia, D. (2021). Charged BTZ-type solutions in Eddington-inspired Born-Infeld gravity. J. Cosmol. Astropart. Phys., 11(11), 025–23pp.
Abstract: We construct an axially symmetric solution of Eddington-inspired Born-Infeld gravity coupled to an electromagnetic field in 2 + 1 dimensions including a (negative) cosmological constant term. This is achieved by using a recently developed mapping procedure that allows to generate solutions in certain families of metric-affine gravity theories starting from a known seed solution of General Relativity, which in the present case corresponds to the electrically charged Banados-Teitelboim-Zanelli (BTZ) solution. We discuss the main features of the new configurations, including the modifications to the ergospheres and horizons, the emergence of wormhole structures, and the consequences for the regularity (or not) of these space-times via geodesic completeness.
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