2025/03/19 by D. L. Canedo, Canedo, D. L., Paulo Vargas Moniz +3
Mathematics · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2503.15348
openalex publication_date 2025/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we apply fractional calculus to study quantum cosmology. Specifically, our Wheeler-DeWitt equation includes a FRW geometry, a radiation fluid, a positive cosmological constant, and an ad hoc potential; we employ the Riesz fractional derivative, which brings a parameter α, where 1 < α≤ 2, appearing explicitly in the mentioned equation. We investigate numerically the tunnelling probability for the Universe to emerge using a suitable WKB approximation. Our findings are as follows. When we decrease the value for α, the tunnelling 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. Concretely, the probability transition in the former if, e.g., Λ=0.7, is very close to the value computed if in the latter we employ instead, e.g., Λ=1.5 and α=1.9397961.