  In contrast to the phenomenon of nullification of the cosmological constant
in the equilibrium vacuum, which is the general property of any quantum vacuum,
there are many options in modifying the Einstein equation to allow the
cosmological constant to evolve in a non-equilibrium vacuum. An attempt is made
to extend the Einstein equation in the direction suggested by the
condensed-matter analogy of the quantum vacuum. Different scenarios are found
depending on the behavior of and the relation between the relaxation parameters
involved, some of these scenarios having been discussed in the literature. One
of them reproduces the scenario in which the effective cosmological constant
emerges as a constant of integration. The second one describes the situation,
when after the cosmological phase transition the cosmological constant drops
from zero to the negative value; this scenario describes the relaxation from
this big negative value back to zero and then to a small positive value. In the
third example the relaxation time is not a constant but depends on matter; this
scenario demonstrates that the vacuum energy (or its fraction) can play the
role of the cold dark matter.
