Evolution of cosmological constant in effective gravity

TL;DR

This paper explores how the cosmological constant can evolve over time within an extended Einstein gravity framework inspired by condensed matter analogies, revealing multiple possible relaxation scenarios.

Contribution

It introduces new models for the evolution of the cosmological constant by modifying Einstein's equations based on quantum vacuum analogies, including scenarios with matter-dependent relaxation.

Findings

The cosmological constant can emerge as a constant of integration.

It can relax from a negative value back to zero and then to a small positive value.

Vacuum energy may act as cold dark matter.

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.