Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied
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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/Math...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/6/349 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849433407377899520 |
|---|---|
| author | Daniel L. Canedo Paulo Moniz Gil Oliveira-Neto |
| author_facet | Daniel L. Canedo Paulo Moniz Gil Oliveira-Neto |
| author_sort | Daniel L. Canedo |
| collection | DOAJ |
| description | 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>), and an <i>ad-hoc</i> potential. We employ the Riesz fractional derivative, which introduces a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>α</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula> (in a non-fractional conventional set-up) versus balancing, e.g., both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> in the fractional framework. |
| format | Article |
| id | doaj-art-e1333e7b7e25450d9d2767f2a6ba8b69 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-e1333e7b7e25450d9d2767f2a6ba8b692025-08-20T03:27:02ZengMDPI AGFractal and Fractional2504-31102025-05-019634910.3390/fractalfract9060349Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative AppliedDaniel L. Canedo0Paulo Moniz1Gil Oliveira-Neto2Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora 36036-330, MG, BrazilDepartamento de Física, Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6200 Covilhã, PortugalDepartamento de Física, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora 36036-330, MG, BrazilIn 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>), and an <i>ad-hoc</i> potential. We employ the Riesz fractional derivative, which introduces a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>α</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, the tunneling probability also decreases, suggesting that if fractional features could be considered to ascertain among different early universe scenarios, then the value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> (meaning strict locality and standard cosmology) would be the most likely. Finally, our results also allow for an interesting discussion between selecting values for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula> (in a non-fractional conventional set-up) versus balancing, e.g., both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> in the fractional framework.https://www.mdpi.com/2504-3110/9/6/349fractional calculusquantum cosmologytunneling probabilitiesdark energy |
| spellingShingle | Daniel L. Canedo Paulo Moniz Gil Oliveira-Neto Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied Fractal and Fractional fractional calculus quantum cosmology tunneling probabilities dark energy |
| title | Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied |
| title_full | Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied |
| title_fullStr | Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied |
| title_full_unstemmed | Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied |
| title_short | Quantum Creation of a Friedmann-Robertson-Walker Universe: Riesz Fractional Derivative Applied |
| title_sort | quantum creation of a friedmann robertson walker universe riesz fractional derivative applied |
| topic | fractional calculus quantum cosmology tunneling probabilities dark energy |
| url | https://www.mdpi.com/2504-3110/9/6/349 |
| work_keys_str_mv | AT daniellcanedo quantumcreationofafriedmannrobertsonwalkeruniverserieszfractionalderivativeapplied AT paulomoniz quantumcreationofafriedmannrobertsonwalkeruniverserieszfractionalderivativeapplied AT giloliveiraneto quantumcreationofafriedmannrobertsonwalkeruniverserieszfractionalderivativeapplied |