Cervantes-Cota, J. L., de Putter, R., & Linder, E. V. (2010). Induced gravity and the attractor dynamics of dark energy/dark matter. J. Cosmol. Astropart. Phys., 12(12), 019–20pp.
Abstract: Attractor solutions that give dynamical reasons for dark energy to act like the cosmological constant, or behavior close to it, are interesting possibilities to explain cosmic acceleration. Coupling the scalar field to matter or to gravity enlarges the dynamical behavior; we consider both couplings together, which can ameliorate some problems for each individually. Such theories have also been proposed in a Higgs-like fashion to induce gravity and unify dark energy and dark matter origins. We explore restrictions on such theories due to their dynamical behavior compared to observations of the cosmic expansion. Quartic potentials in particular have viable stability properties and asymptotically approach general relativity.
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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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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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Izadi, A., Shacker, S. S., Olmo, G. J., & Banerjee, R. (2018). Observational effects of varying speed of light in quadratic gravity cosmological models. Int. J. Geom. Methods Mod. Phys., 15(5), 1850084–16pp.
Abstract: We study different manifestations of the speed of light in theories of gravity where metric and connection are regarded as independent fields. We find that for a generic gravity theory in a frame with locally vanishing affine connection, the usual degeneracy between different manifestations of the speed of light is broken. In particular, the space-time causal structure constant (c(ST)) may become variable in that local frame. For theories of the form f(R, R-mu nu R-mu nu), this variation in c(ST) has an impact on the definition of the luminosity distance (and distance modulus), which can be used to confront the predictions of particular models against Supernovae type Ia (SN Ia) data. We carry out this test for a quadratic gravity model without cosmological constant assuming (i) a constant speed of light and (ii) a varying speed of light (VSL), and find that the latter scenario is favored by the data.
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Olmo, G. J. (2011). Palatini approach to modified gravity: f(R) theories and beyond. Int. J. Mod. Phys. D, 20(4), 413–462.
Abstract: We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speed-up problem, laboratory and solar system tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other phenomenological aspects related with dark matter/energy and quantum gravity.
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