The virial theorem and the dark matter problem in hybrid metric-Palatini gravity

Abstract

Hybrid metric-Palatini gravity is a recently proposed theory, consisting of\nthe superposition of the metric Einstein-Hilbert Lagrangian with an $f(\\cal R)$\nterm constructed \\`{a} la Palatini. The theory predicts the existence of a\nlong-range scalar field, which passes the Solar System observational\nconstraints, even if the scalar field is very light, and modifies the\ncosmological and galactic dynamics. Thus, the theory opens new possibilities to\napproach, in the same theoretical framework, the problems of both dark energy\nand dark matter. In this work, we consider the generalized virial theorem in\nthe scalar-tensor representation of the hybrid metric-Palatini gravity. More\nspecifically, taking into account the relativistic collisionless Boltzmann\nequation, we show that the supplementary geometric terms in the gravitational\nfield equations provide an effective contribution to the gravitational\npotential energy. We show that the total virial mass is proportional to the\neffective mass associated with the new terms generated by the effective scalar\nfield, and the baryonic mass. This shows that the geometric origin in the\ngeneralized virial theorem may account for the well-known virial theorem mass\ndiscrepancy in clusters of galaxies. In addition to this, we also consider\nastrophysical applications of the model and show that the model predicts that\nthe mass associated to the scalar field and its effects extend beyond the\nvirial radius of the clusters of galaxies. In the context of the galaxy cluster\nvelocity dispersion profiles predicted by the hybrid metric-Palatini model, the\ngeneralized virial theorem can be an efficient tool in observationally testing\nthe viability of this class of generalized gravity models.\n