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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Girones, Z., Marchetti, A., Mena, O., Pena-Garay, C., & Rius, N. (2010). Cosmological data analysis of f(R) gravity models. J. Cosmol. Astropart. Phys., 11(11), 004–18pp.
Abstract: A class of well-behaved modified gravity models with long enough matter domination epoch and a late-time accelerated expansion is confronted with SNIa, CMB, SDSS, BAO and H(z) galaxy ages data, as well as current measurements of the linear growth of structure. We show that the combination of geometrical probes and growth data exploited here allows to rule out f(R) gravity models, in particular, the logarithmic of curvature model. We also apply solar system tests to the models in agreement with the cosmological data. We find that the exponential of the inverse of the curvature model satisfies all the observational tests considered and we derive the allowed range of parameters. Current data still allows for small deviations of Einstein gravity. Future, high precision growth data, in combination with expansion history data, will be able to distinguish tiny modifications of standard gravity from the Lambda CDM model.
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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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Creminelli, P., Norena, J., Pena, M., & Simonovic, M. (2012). Khronon inflation. J. Cosmol. Astropart. Phys., 11(11), 032–16pp.
Abstract: We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t -> (t) over tilde (t), or equivalently under field redefinition of the inflaton phi -> (phi) over tilde(phi). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k(L) in the squeezed limit k(L) -> 0 compared to the local shape.
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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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