Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied
Year: 2025
Type: article
Abstract: In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt (WDW) equation includes a Friedman-Robertson-Walker (FRW) geometry, a radiation fluid, a positive cosmological constant (Λ), and an ad-hoc potential. We employ the Riesz fractional derivative, which introduces a parameter α, where 1<α≤2, in the WDW equation. We investigate numerically the tunneling probability for the Universe to emerge using a suitable WKB approximation. Our findings are as follows. When we decrease the value of α, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value α=2 (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for Λ (in a non-fractional conventional set-up) versus balancing, e.g., both Λ and α in the fractional framework.
Source: Fractal and Fractional
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
Funders: Centro de Matemática e Aplicações da Universidade da Beira Interior, Universidade da Beira Interior, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Fundação de Amparo à Pesquisa do Estado de Minas Gerais, Universidade Federal de Juiz de Fora, Fundação para a Ciência e a Tecnologia
OpenAlex ID: W4410761406