Fundamental constants and cosmic vacuum: The micro and macro connection

The idea that the vacuum energy density rho(Lambda) could be time-dependent is a most reasonable one in the expanding Universe; in fact, much more reasonable than just a rigid cosmological constant for the entire cosmic history. Being rho(Lambda) = rho(Lambda)(t) dynamical, it offers a possibility to tackle the cosmological constant problem in its various facets. Furthermore, for a long time (most prominently since Dirac's first proposal on a time variable gravitational coupling) the possibility that the fundamental "constants" of Nature are slowly drifting with the cosmic expansion has been continuously investigated. In the last two decades, and specially in recent times, mounting experimental evidence attests that this could be the case. In this paper, we consider the possibility that these two groups of facts might be intimately connected, namely that the observed acceleration of the Universe and the possible time variation of the fundamental constants are two manifestations of the same underlying dynamics. We call it: the "micro and macro connection", and on its basis we expect that the cosmological term in Einstein's equations, Newton's coupling and the masses of all the particles in the Universe, both the dark matter (DM) particles and the ordinary baryons and leptons, should all drift with the cosmic expansion. Here, we discuss specific cosmological models realizing such possibility in a way that preserves the principle of covariance of general relativity (GR).