de Sitter Fractional Quantum Cosmology

TL;DR

This paper introduces a fractional quantum cosmology approach using Riesz's fractional derivative in the Wheeler--DeWitt equation, revealing how different wavefunctions influence the fractal nature and evolution of the universe.

Contribution

It applies fractional derivatives to quantum cosmology, providing new insights into the fractal structure and evolution of the universe in different boundary condition proposals.

Findings

Tunneling wavefunction favors fractal dimensions less than 2.5 and an accelerated phase.

No-boundary wavefunction favors fractal dimensions close to 3 and a decelerated universe.

Flat or open universes are more probable than closed inflationary models in fractional quantum cosmology.

Abstract

We employ Riesz's fractional derivative into the Wheeler--DeWitt equation for a closed de Sitter geometry and obtain the no-boundary and tunneling wavefunctions. From the corresponding probability distributions, the event horizon of the nucleated universe can be a fractal surface with dimensions between $2\leq D<3$. Concretely, the tunneling wavefunction favors fractal dimensions less than $2.5$ and an accelerated power-law phase. Differently, the no-boundary proposal conveys fractal dimensions close to $3$, with the universe instead entering a decelerated phase. Subsequently, we extend our discussion towards (non-trivial compact) flat and open scenarios. Results suggest that given the probability of creation of a closed inflationary universe in the tunneling proposal is exponentially suppressed, a flat or an open universe becomes favored within fractional inflationary quantum universe.