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.

arXiv comment15 pages, 8 figures. Moderate revision. Matches the version accepted for publication in MNRAS

References in corpus (44)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• emcee: The MCMC Hammer
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• The Cosmological Constant
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• A 6% measurement of the Hubble parameter at $z\sim 0.45$: direct evidence of the epoch of cosmic re-acceleration
• Dynamical dark energy in light of the latest observations
• Fractal universe and quantum gravity
• To H0 or not to H0?
• Review of Some Promising Fractional Physical Models
• Quantum field theory, gravity and cosmology in a fractal universe
• Running Hubble Tension and a H0 Diagnostic
• Cosmology Intertwined IV: The Age of the Universe and its Curvature
• Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics
• Multifractional theories: an unconventional review
• Multi-scale gravity and cosmology
• Cosmological Models with Fractional Derivatives and Fractional Action Functional
• MOND-like Fractional Laplacian Theory
• Quantum gravity and gravitational-wave astronomy
• The Age of the Universe with Globular Clusters: Reducing Systematic Uncertainties
• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• de Sitter Fractional Quantum Cosmology
• Fractional Action Cosmology: Emergent, Logamediate, Intermediate, Power law Scenarios of the Universe and Generalized Second Law of Thermodynamics
• Stochastic gravitational-wave background in quantum gravity
• From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
• Fractional Action Cosmology with Power Law Weight Function
• Testing Fractional Action Cosmology
• Fractional Action Cosmology: Some Dark Energy Models in Emergent, Logamediate and Intermediate Scenarios of the Universe
• Fractional Nonholonomic Ricci Flows
• Multifractional theories: an updated review
• Cosmic microwave background and inflation in multi-fractional spacetimes
• Fractional Einstein-Hilbert Action Cosmology
• Broadening quantum cosmology with a fractional whirl
• Timelike self-similar spherically symmetric perfect-fluid models
• Complex dimensions and their observability
• Fractional-order derivatives in cosmological models of accelerated expansion
• Quantum scalar field theories with fractional operators
• Dark energy in multi-fractional spacetimes
• Cosmic Evolution in Fractional Action Cosmology
• Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe
• Spatially self-similar locally rotationally symmetric perfect fluid models
• Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative
• New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity

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• Estimated Age of the Universe in Fractional Cosmology
• Quantum fractionary cosmology: K-essence theory
• Dark Universe Phenomenology from Yukawa Potential?
• An exponential equation of state of dark energy in the light of 2018 CMB Planck data
• Modified Friedmann equations from fractional entropy
• Emergence of fractal cosmic space from fractional quantum gravity
• Conformal and Non-Minimal Couplings in Fractional Cosmology
• Dark Matter in Fractional Gravity I: Astrophysical Tests on Galactic Scales
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• Reconstructing FHDE with Scalar and Gauge Fields
• Cosmological impact of microwave background temperature measurements
• Fractional Einstein field equations in $2+1$ dimensional spacetime
• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
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• Constraining fractionality using some observational tests