  We discuss the main myths related to the vacuum energy and cosmological
constant, such as: ``unbearable lightness of space-time''; the dominating
contribution of zero point energy of quantum fields to the vacuum energy;
non-zero vacuum energy of the false vacuum; dependence of the vacuum energy on
the overall shift of energy; the absolute value of energy only has significance
for gravity; the vacuum energy depends on the vacuum content; cosmological
constant changes after the phase transition; zero-point energy of the vacuum
between the plates in Casimir effect must gravitate, that is why the zero-point
energy in the vacuum outside the plates must also gravitate; etc. All these and
some other conjectures appear to be wrong when one considers the thermodynamics
of the ground state of the quantum many-body system, which mimics macroscopic
thermodynamics of quantum vacuum. In particular, in spite of the ultraviolet
divergence of the zero-point energy, the natural value of the vacuum energy is
comparable with the observed dark energy. That is why the vacuum energy is the
plausible candidate for the dark energy.
