de Sitter 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 ≤ 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.