
Capozziello, S., Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2013). Galactic rotation curves in hybrid metricPalatini gravity. Astropart Phys., 5052, 65–75.
Abstract: Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence of a constant velocity region, near the baryonic matter distribution, followed by a quick decay at large distances. In this work, we consider the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained within the framework of the recently proposed hybrid metricPalatini gravitational theory. The latter is constructed by modifying the metric EinsteinHilbert action with an f(R) term in the Palatini formalism. It was shown that the theory unifies local constraints and the latetime cosmic acceleration, even if the scalar field is very light. In the intermediate galactic scale, we show explicitly that in the hybrid metricPalatini model the tangential velocity can be explicitly obtained as a function of the scalar field of the equivalent scalartensor description. The model predictions are compared model with a small sample of rotation curves of low surface brightness galaxies, respectively, and a good agreement between the theoretical rotation Curves and the observational data is found. The possibility of constraining the form of the scalar field and the parameters of the model by using the stellar velocity dispersions is also analyzed. Furthermore, the Doppler velocity shifts are also obtained in terms of the scalar field. All the physical and geometrical quantities and the numerical parameters in the hybrid metricPalatini model can be expressed in terms of observable/measurable parameters, such as the tangential velocity, the baryonic mass of the galaxy, the Doppler frequency shifts, and the stellar dispersion velocity, respectively. Therefore, the obtained results open the possibility of testing the hybrid metricPalatini gravitational models at the galactic or extragalactic scale by using direct astronomical and astrophysical observations.



Capozziello, S., Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2013). Cosmology of hybrid metricPalatini 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 EinsteinHilbert Lagrangian with an f(R) term constructed a la Palatini was proposed recently. The dynamically equivalent scalartensor 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 longrange 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 T2 + R, where T and R are the traces of the stressenergy 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 metricPalatini gravitational theory are also explored, and cosmological solutions coming from the scalartensor 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 largescale structure.



Capozziello, S., Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2013). The virial theorem and the dark matter problem in hybrid metricPalatini gravity. J. Cosmol. Astropart. Phys., 07(7), 024–19pp.
Abstract: Hybrid metricPalatini gravity is a recently proposed theory, consisting of the superposition of the metric EinsteinHilbert Lagrangian with an f(R) term constructed a la Palatini. The theory predicts the existence of a longrange scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics. Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter. In this work, we consider the generalized virial theorem in the scalartensor representation of the hybrid metricPalatini gravity. More specifically, taking into account the relativistic collisionless Boltzmann equation, we show that the supplementary geometric terms in the gravitational field equations provide an effective contribution to the gravitational potential energy. We show that the total virial mass is proportional to the effective mass associated with the new terms generated by the effective scalar field, and the baryonic mass. In addition to this, we also consider astrophysical applications of the model and show that the model predicts that the mass associated to the scalar field and its effects extend beyond the virial radius of the clusters of galaxies. In the context of the galaxy cluster velocity dispersion profiles predicted by the hybrid metricPalatini model, the generalized virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.



Capozziello, S., Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2012). Wormholes supported by hybrid metricPalatini gravity. Phys. Rev. D, 86(12), 127504–5pp.
Abstract: Recently, a modified theory of gravity was presented, which consists of the superposition of the metric EinsteinHilbert Lagrangian with an f(R) term constructed a la Palatini. The theory possesses extremely interesting features such as predicting the existence of a longrange scalar field, that explains the latetime cosmic acceleration and passes the local tests, even in the presence of a light scalar field. In this brief report, we consider the possibility that wormholes are supported by this hybrid metricPalatini gravitational theory. We present here the general conditions for wormhole solutions according to the null energy conditions at the throat and find specific examples. In the first solution, we specify the redshift function, the scalar field and choose the potential that simplifies the modified KleinGordon equation. This solution is not asymptotically flat and needs to be matched to a vacuum solution. In the second example, by adequately specifying the metric functions and choosing the scalar field, we find an asymptotically flat spacetime.



Capozziello, S., Harko, T., Lobo, F. S. N., & Olmo, G. J. (2013). Hybrid Modified Gravity Unifying Local Tests, Galactic Dynamics and LateTime Cosmic Acceleration. Int. J. Mod. Phys. D, 22(12), 1342006–7pp.
Abstract: The nonequivalence between the metric and Palatini formalisms of f(R) gravity is an intriguing feature of these theories. However, in the recently proposed hybrid metricPalatini gravity, consisting of the superposition of the metric EinsteinHilbert Lagrangian with an f(R) term constructed a la Palatini, the “true” gravitational field is described by the interpolation of these two nonequivalent approaches. The theory predicts the existence of a light longrange scalar field, which passes the local constraints and affects the galactic and cosmological dynamics. Thus, the theory opens new possibilities for a unified approach, in the same theoretical framework, to the problems of dark energy and dark matter, without distinguishing a priori matter and geometric sources, but taking their dynamics into account under the same standard.



Capozziello, S., Harko, T., Lobo, F. S. N., Olmo, G. J., & Vignolo, S. (2014). The Cauchy problem in hybrid metricPalatini f(X)gravity. Int. J. Geom. Methods Mod. Phys., 11(5), 1450042–12pp.
Abstract: The wellformulation and the wellposedness of the Cauchy problem are discussed for hybrid metricPalatini gravity, a recently proposed modified gravitational theory consisting of adding to the EinsteinHilbert Lagrangian an f(R)term constructed a la Palatini. The theory can be recast as a scalartensor one predicting the existence of a light longrange scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the latetime cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be wellformulated and, furthermore, can be wellposed depending on the adopted matter sources.

