  The cosmological constant is not an absolute constant. The gravitating part
of the vacuum energy is adjusted to the energy density of matter and to other
types of the perturbations of the vacuum. We discuss how the vacuum energy
responds (i) to the curvature of space in the Einstein closed Universe; (ii) to
the expansion rate in the de Sitter Universe; and (iii) to the rotation in the
Goedel Universe. In all these steady state Universes, the gravitating vacuum
energy is zero in the absence of the perturbation, and is proportional to the
energy density of perturbation. This is in a full agreement with the
thermodynamic Gibbs-Duhem relation applicable to any quantum vacuum. It
demonstrates that (i) the cosmological constant is not huge, since according to
the Gibbs-Duhem relation the contribution of zero point fluctuations to the
vacuum energy is cancelled by the trans-Planckian degrees of freedom; (ii) the
cosmological constant is non-zero, since the perturbations of the vacuum state
induce the non-zero vacuum energy; and (iii) the gravitating vacuum energy is
on the order of the energy density of matter and/or of other perturbations. We
also consider the vacuum response to the non-steady-state perturbations. In
this case the Einstein equations are modified to include the non-covariant
corrections, which are responsible for the relaxation of the cosmological
constant. The connection to the quintessence is demonstrated. The problem of
the energy-momentum tensor for the gravitational field is discussed in terms of
effective gravity. The difference between the momentum and pseudo-momentum of
gravitational waves in general relativity is similar to that for sound waves in
hydrodynamics.
