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Anisotropic Fractional Cosmology: K-Essence Theory
Version 1
: Received: 15 September 2023 / Approved: 18 September 2023 / Online: 19 September 2023 (15:23:55 CEST)
A peer-reviewed article of this Preprint also exists.
Socorro, J.; Rosales, J.J.; Toledo-Sesma, L. Anisotropic Fractional Cosmology: K-Essence Theory. Fractal Fract. 2023, 7, 814. Socorro, J.; Rosales, J.J.; Toledo-Sesma, L. Anisotropic Fractional Cosmology: K-Essence Theory. Fractal Fract. 2023, 7, 814.
Abstract
In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation
for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also
given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$,
however in the dust era we found a closed solution in the gauge time $\tau$.
Keywords
Fractional derivative; Fractional Quantum Cosmology; K-essence formalism; Classical and Quantum exact solutions
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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