Cosmology under the fractional calculus approach
| Title: | Cosmology under the fractional calculus approach |
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| Authors: | García-Aspeitia, Miguel A., Fernandez-Anaya, Guillermo, Hernández-Almada, A., Leon, Genly, Magaña, Juan |
| Publication Year: | 2022 |
| Collection: | Astrophysics General Relativity and Quantum Cosmology |
| Subject Terms: | General Relativity and Quantum Cosmology, Astrophysics - Cosmology and Nongalactic Astrophysics |
| More Details: | Fractional cosmology modifies the standard derivative to Caputo's fractional derivative of order $\mu$, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on $\mu$ and the age of the Universe $t_U$. We estimate stringent constraints on $\mu$ using cosmic chronometers, Type Ia supernovae, and joint analysis. We obtain $\mu=2.839^{+0.117}_{-0.193}$ within the $1\sigma$ confidence level providing a non-standard cosmic acceleration at late times; consequently, the Universe would be older than the standard estimations. Additionally, we present a stability analysis for different $\mu$ values. This analysis identifies a late-time attractor corresponding to a power-law decelerated solution for $\mu < 2$. Moreover, a non-relativistic critical point exists for $\mu > 1$ and a sink for $\mu > 2$. This solution is a decelerated power-law if $1 < \mu < 2$ and an accelerated power-law solution if $\mu > 2$, consistent with the mean values obtained from the observational analysis. Therefore, for both flat FLRW and Bianchi I metrics, the modified Friedmann equations provide a late cosmic acceleration under this paradigm without introducing a dark energy component. This approach could be a new path to tackling unsolved cosmological problems. Comment: 15 pages, 8 figures. Moderate revision. Matches the version accepted for publication in MNRAS |
| Document Type: | Working Paper |
| DOI: | 10.1093/mnras/stac3006 |
| Access URL: | http://arxiv.org/abs/2207.00878 |
| Accession Number: | edsarx.2207.00878 |
| Database: | arXiv |
| DOI: | 10.1093/mnras/stac3006 |
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