Cosmologies with a time dependent vacuum

The idea that the cosmological term, Lambda, 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, namely one that has remained immutable since the origin of time. A smoothly evolving vacuum energy density that inherits its time-dependence from cosmological functions, such as the Hubble rate or the scale factor, 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" Lambda 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 of the dark energy could be evolving with time/redshift (including the possibility that it might currently behave phantom-like) suggests that a time-variable Lambda term (possibly accompanied by a variable Newton's gravitational coupling 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.