O problema da matéria escura e o teorema do virial na teoria de gravidade Eddington-Born-Infeld

Dark matter is a fundamental ingredient of the modern Cosmology. It is necessary in order to explain the process of structures formation in the Universe, rotation curves of galaxies and the mass discrepancy in clusters of galaxies. However, although many efforts, in both aspects, theoretical and experimental, have been made, the nature of dark matter is still unknown and the only convincing evidence for its existence is gravitational. This rises doubts about its existence and, in turn, opens the possibility that the Einstein’s gravity needs to be modified at some scale. We study, in this work, the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides en alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations and find their solutions to a spherical system of identical and collisionless point particles. Then, we took into account the collisionless relativistic Boltzmann equation and using some approximations and assumptions for weak gravitational field, we derived the generalized virial theorem in the framework of EBI gravity. In order to compare the predictions of EBI gravity with astrophysical observations we estimated the order of magnitude of the geometric mass, showing that it is compatible with present observations. Finally, considering a power law for the density of galaxies in the cluster, we derived expressions for the radial velocity dispersion of the galaxies, which can be used for testing some features of the EBI gravity.

O problema da matéria escura e o teorema do virial na teoria de gravidade Eddington-Born-Infeld

Dark matter is a fundamental ingredient of the modern Cosmology. It is necessary in order to explain the process of structures formation in the Universe, rotation curves of galaxies and the mass discrepancy in clusters of galaxies. However, although many efforts, in both aspects, theoretical and experimental, have been made, the nature of dark matter is still unknown and the only convincing evidence for its existence is gravitational. This rises doubts about its existence and, in turn, opens the possibility that the Einstein’s gravity needs to be modified at some scale. We study, in this work, the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides en alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations and find their solutions to a spherical system of identical and collisionless point particles. Then, we took into account the collisionless relativistic Boltzmann equation and using some approximations and assumptions for weak gravitational field, we derived the generalized virial theorem in the framework of EBI gravity. In order to compare the predictions of EBI gravity with astrophysical observations we estimated the order of magnitude of the geometric mass, showing that it is compatible with present observations. Finally, considering a power law for the density of galaxies in the cluster, we derived expressions for the radial velocity dispersion of the galaxies, which can be used for testing some features of the EBI gravity.