Quantum corrections to the dynamics of the expanding universe

TL;DR

This paper explores how quantum effects influence the dynamics of the expanding universe, suggesting that dark matter and dark energy could originate from quantum phenomena, and derives modified Einstein equations incorporating quantum sources.

Contribution

It introduces a quantum geometrodynamical model that modifies Einstein's equations with quantum sources and analyzes the quantum origin of dark matter and dark energy.

Findings

Quantum corrections can significantly affect cosmic evolution.

Scalar fields can behave as Weyssenhoff fluids with quantum properties.

Quantum effects may be responsible for dark matter and dark energy.

Abstract

The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation complemented by the equations of motion for the momentum operator and its time derivative in Heisenberg's form reduce to the Einstein equations with an additional source of the gravitational field of quantum nature. The spatially closed universe with cosmological constant, originally filled with a uniform scalar field and radiation, is considered as quantum cosmological system. The perfect fluid in the form of radiation defines the material reference frame. The properties of the averaged scalar field which acts like ordinary matter are investigated. After averaging over its quantum states, the free scalar field turns into the Weyssenhoff fluid characterized by the energy density, pressure, and spin of constituent particles. The cases when the contribution of the quantum effects into the gravitational interaction becomes significant on macroscopic scale are analyzed. It is demonstrated that, unless the whole, at least a part of such matter-energy constituents as dark matter and dark energy may have a quantum origin.