Cosmological constant and vacuum energy: old and new ideas
  The cosmological constant (CC) term in Einstein's equations, Lambda, was
first associated to the idea of vacuum energy density. Notwithstanding, it is
well-known that there is a huge, in fact appalling, discrepancy between the
theoretical prediction and the observed value picked from the modern
cosmological data. This is the famous, and extremely difficult, "CC problem".
Paradoxically, the recent observation at the CERN Large Hadron Collider of a
Higgs-like particle, should actually be considered ambivalent: on the one hand
it appears as a likely great triumph of particle physics, but on the other hand
it wide opens Pandora's box of the cosmological uproar, for it may provide
(alas!) the experimental certification of the existence of the electroweak (EW)
vacuum energy, and thus of the intriguing reality of the CC problem. Even if
only counting on this contribution to the inventory of vacuum energies in the
universe, the discrepancy with the cosmologically observed value is already of
55 orders of magnitude. This is the (hitherto) "real" magnitude of the CC
problem, rather than the (too often) brandished 123 ones from the upper (but
fully unexplored!) ultrahigh energy scales. Such is the baffling situation
after 96 years of introducing the Lambda-term by Einstein. In the following I
will briefly (and hopefully pedagogically) fly over some of the old and new
ideas on the CC problem. Since, however, the Higgs boson just knocked our door
and recalled us that the vacuum energy may be a fully tangible concept in real
phenomenology, I will exclusively address the CC problem from the original
notion of vacuum energy, and its possible "running" with the expansion of the
universe, rather than venturing into the numberless attempts to replace the CC
by the multifarious concept of dark energy.
