Cosmology under the fractional calculus approach

Abstract

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 $\mu =2.839_{-0.193}^{+0.117}$ 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.

15 pages, 8 figures. Moderate revision. Matches the version accepted for publication in MNRAS

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Cited by in corpus (8)

• Revisiting Fractional Cosmology
• Exact solutions and cosmological constraints in fractional cosmology
• Quantum fractionary cosmology: K-essence theory
• Emergence of fractal cosmic space from fractional quantum gravity
• Modified Friedmann equations from fractional entropy
• Conformal and Non-Minimal Couplings in Fractional Cosmology
• Dark Matter in Fractional Gravity I: Astrophysical Tests on Galactic Scales
• Cosmological impact of microwave background temperature measurements