Evolution of cosmological constant in effective gravity

G. E. Volovik

*Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland*

Landau Institute for Theoretical Physics RAS, 117334 Moscow, Russia

PACS: 04.90.+e, 98.80.-k

**Abstract**

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.