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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2503.15348 |
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| author | Canedo, D. L. Moniz, P. Oliveira-Neto, G. |
| author_facet | Canedo, D. L. Moniz, P. Oliveira-Neto, G. |
| contents | 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 $1 < α\leq 2$, 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 $α=1.9397961$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Creation of a FRW Universe: applying the Riesz fractional derivative Canedo, D. L. Moniz, P. Oliveira-Neto, G. General Relativity and Quantum Cosmology 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 $1 < α\leq 2$, 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 $α=1.9397961$. |
| title | Quantum Creation of a FRW Universe: applying the Riesz fractional derivative |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2503.15348 |