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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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Capozziello, S., Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2013). Cosmology of hybrid metric-Palatini f(X)-gravity. J. Cosmol. Astropart. Phys., 04(4), 011–25pp.
Abstract: A new class of modified theories of gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed a la Palatini was proposed recently. The dynamically equivalent scalar-tensor representation of the model was also formulated, and it was shown that even if the scalar field is very light, the theory passes the Solar System observational constraints. Therefore the model predicts the existence of a long-range scalar field, modifying the cosmological and galactic dynamics. An explicit model that passes the local tests and leads to cosmic acceleration was also obtained. In the present work, it is shown that the theory can be also formulated in terms of the quantity X equivalent to kappa T-2 + R, where T and R are the traces of the stress-energy and Ricci tensors, respectively. The variable X represents the deviation with respect to the field equation trace of general relativity. The cosmological applications of this hybrid metric-Palatini gravitational theory are also explored, and cosmological solutions coming from the scalar-tensor representation of f(X)-gravity are presented. Criteria to obtain cosmic acceleration are discussed and the field equations are analyzed as a dynamical system. Several classes of dynamical cosmological solutions, depending on the functional form of the effective scalar field potential, describing both accelerating and decelerating Universes are explicitly obtained. Furthermore, the cosmological perturbation equations are derived and applied to uncover the nature of the propagating scalar degree of freedom and the signatures these models predict in the large-scale structure.
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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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Simpson, F., Jimenez, R., Pena-Garay, C., & Verde, L. (2018). Dark energy from the motions of neutrinos. Phys. Dark Universe, 20, 72–77.
Abstract: Ordinarily, a scalar field may only play the role of dark energy if it possesses a potential that is either extraordinarily flat or extremely fine-tuned. Here we demonstrate that these restrictions are lifted when the scalar field undergoes persistent energy exchange with another fluid. In this scenario, the field is prevented from reversing its direction of motion, and instead may come to rest while displaced from the local minimum of its potential. Therefore almost any scalar potential is capable of initiating a prolonged phase of cosmic acceleration. If the rate of energy transfer is modulated via a derivative coupling, the field undergoes a rapid process of freezing, after which the field's equation of state mimicks that of a cosmological constant. We present a physically motivated realisation in the form of a neutrino-majoron coupling, which avoids the dynamical instabilities associated with mass-varying neutrino models. Finally we discuss possible means by which this model could be experimentally verified.
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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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