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 $2\le D<3$. 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.

arXiv comment7 pages, 1 figure, to appear in Phys. Rev. D

References in corpus (21)

• Fractional Quantum Mechanics and Levy Path Integrals
• Planck 2013 results. XXII. Constraints on inflation
• Fractional Quantum Mechanics
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Towards singularity and ghost free theories of gravity
• Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes
• Spectral Dimension of the Universe
• Fractal universe and quantum gravity
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Approaches to Quantum Cosmology
• Quantum field theory, gravity and cosmology in a fractal universe
• Fractal Structure of Loop Quantum Gravity
• Creation of a Compact Topologically Nontrivial Inflationary Universe
• Time Fractional Quantum Mechanics
• Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics
• The wave function discord
• Quantum Cosmology and Open Universes
• On the problem of initial conditions for inflation
• From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
• Broadening quantum cosmology with a fractional whirl
• Fractional Derivative Regularization in QFT

Cited by in corpus (20)

• Cosmology under the fractional calculus approach
• Inflation and fractional quantum cosmology
• Imprints of Barrow-Tsallis Cosmology in Primordial Gravitational Waves
• Revisiting Fractional Cosmology
• Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles
• Exact solutions and cosmological constraints in fractional cosmology
• Estimated Age of the Universe in Fractional Cosmology
• Modified cosmology from quantum deformed entropy
• Quantum fractionary cosmology: K-essence theory
• Barrow and Tsallis entropies after the DESI DR2 BAO data
• Emergence of fractal cosmic space from fractional quantum gravity
• Modified Friedmann equations from fractional entropy
• Conformal and Non-Minimal Couplings in Fractional Cosmology
• Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon
• On the thermodynamics of reconciling quantum and gravity
• Fractional Einstein field equations in $2+1$ dimensional spacetime
• Holographic vacuum energy regularization and corrected entropy of de Sitter space
• Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity
• Inflation and Primordial Perturbations in Fractal Cosmology
• Cosmology of fractional gravity