Cosmologies with a time dependent vacuum

The idea that the cosmological term A should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, rho(Lambda) = Lambda/(8 pi G), namely one that has remained immutable since the origin of time. A smoothly evolving vacuum energy density rho(Lambda) = rho(Lambda)(xi(t)) that inherits its time-dependence from cosmological functions xi = xi(t), such as the Hubble rate H(t) or the scale factor a(t), is not only a qualitatively more plausible and intuitive idea, but is also suggested by fundamental physics, in particular by quantum field theory (QFT) in curved space-time. To implement this notion, is not strictly necessary to resort to ad hoc scalar fields, as usually done in the literature (e.g. in quintessence formulations and the like). A "running" A term can be expected on very similar grounds as one expects (and observes) the running of couplings and masses with a physical energy scale in QFT. Furthermore, the experimental evidence that the equation of state (EOS) of the dark energy (DE) could be evolving with time/redshift (including the possibility that it might currently behave phantom-like) suggests that a time variable Lambda = Lambda(t) term (possibly accompanied by a variable Newton's gravitational coupling too, G = G (t)) could account in a natural way for all these features. Remarkably enough, a class of these models (the "new cosmon") could even be the clue for solving the old cosmological constant problem, including the coincidence problem.