Inflation and Fractional Quantum Cosmology

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 Wentzel-Kramers-Brillouin (WKB) approximat...

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Bibliographic Details
Published in:Fractal and fractional 2022-11, Vol.6 (11), p.655
Main Authors: Rasouli, Seyed Meraj Mousavi, de Oliveira Costa, Emanuel W., Moniz, Paulo, Jalalzadeh, Shahram
Format: Article
Language:English
Subjects:
Calculus
Cosmology
Fractal geometry
fractional calculus
fractional quantum cosmology
inflation
Inflation (cosmology)
non-locality
Power law
Quantum field theory
Spacetime
Universe
Wheeler–DeWitt equation
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Summary: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 Wentzel-Kramers-Brillouin (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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6110655