Inflation and fractional quantum cosmology

Abstract

The Wheeler--DeWitt equation for a flat and compact Friedmann--Lemaître--Robertson--Walker cosmology at the pre-inflation epoch is studied in the contexts of the standard and fractional quantum cosmology. Working within the semiclassical regime and applying the WKB approximation, we show that some fascinating consequences are obtained for our simple fractional scenario that are completely different from their corresponding standard counterparts: (i) The conventional de Sitter behavior of the inflationary universe for constant potential is replaced by a power-law inflation. (ii) The non-locality of the Riesz's fractional derivative produces a power-law inflation that depends on the fractal dimension of the compact spatial section of space-time, independent of the energy scale of the inflaton.

13 pages

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Cited by in corpus (12)

• Fractional Holographic Dark Energy
• Estimated Age of the Universe in Fractional Cosmology
• Quantum fractionary cosmology: K-essence theory
• Fractional Scalar Field Cosmology
• Emergence of fractal cosmic space from fractional quantum gravity
• Modified Friedmann equations from fractional entropy
• Fractional Schwarzschild-Tangherlini black hole with a fractal event horizon
• Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity
• Phase space noncommutativity, power-law inflation and quantum cosmology
• Inflation and Primordial Perturbations in Fractal Cosmology
• Emergent $\Lambda$CDM cosmology from a measure-induced deformation of the Newtonian action
• Cosmology of fractional gravity