Dynamical Vacuum in Quantum Cosmology

TL;DR

This paper quantizes de Sitter cosmology by treating the vacuum as a dynamical fluid, leading to a natural emergence of the cosmological constant and a time variable, with quantum effects prominent at small scales.

Contribution

It introduces a novel approach where the vacuum's degrees of freedom generate the cosmological constant dynamically, differing from previous static assumptions.

Findings

States with definite cosmological constant do not exist.

Quantum effects are significant at small scale factors.

Classical behavior emerges at large times and scales.

Abstract

By regarding the vacuum as a perfect fluid with equation of state p=-rho, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found. It turns out that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.