Cosmological solutions for the Universe filled with matter in various states and gauge invariance

TL;DR

This paper investigates cosmological models with various matter types, linking matter equations of state to gauge choices, and explores quantum solutions describing different universe evolution stages, including early inflation and late acceleration.

Contribution

It establishes a correspondence between matter equations of state and gauge conditions, and analyzes quantum cosmological solutions for different evolutionary regimes.

Findings

Different matter types correspond to specific gauge conditions.

Quantum solutions describe asymptotic regimes of the Universe.

Early Universe dominated by de Sitter vacuum transitions to radiation-dominated stage.

Abstract

We explore at phenomenological level a model of the Universe filled with various kinds of matter characterized by different equations of state. We show that introducing of each kind of matter is equivalent to a certain choice of a gauge condition, the gauge condition describing a medium with a given equation of state. The case of a particular interest is when one kind of matter (de Sitter false vacuum) dominates at the early stage of the Universe evolution while another kind (radiation, or ultrarelativistic gas) dominates at its later stage. We can, therefore, consider different asymptotic regimes for the early and later stages of the Universe existence. These regimes are described by solutions to the Wheeler - DeWitt equation for the Universe with matter in that given state, and, at the same time, in the "extended phase space" approach to quantum geometrodynamics the regimes are described by solutions to a Schrodinger equation associated with a choice of some gauge condition. It is supposed that, from the viewpoint of the observer located at the later stage of the Universe evolution, solutions for a Lambda-dominated early Universe would decay.