  In this review, I discuss briefly how the presence of a cosmological constant
in the Universe may imply a decoherent evolution of quantum matter in it, and
as a consequence a fundamental irreversibility of time unrelated in principle
to CP properties (Cosmological CPT Violation).In this context, I also discuss
recently suggested novel possible contributions of massive neutrinos to the
cosmological constant, which are not due to the standard loop expansion in
quantum field theory, but rather due to unconventional properties of (some
version of) the quantum theory underlying flavour mixing. It is also argued
that quantum space time foam may be responsible for the neutrino mass
differences, observed today, and through the above considerations, for the
(majority of the) dark energy of the Universe in the present era. In the above
context, I also present a fit of all the currently available neutrino
oscillation data, including the LSND ``anomalous'' experimental results, based
on such a CPT Violating decoherent neutrino model. The key feature is to use
different decoherent parameters between neutrinos and antineutrinos, due to the
above mentioned CPT violation. This points to the necessity of future
experiments, concentrating on the antineutrino sector, in order to falsify the
model.
