2023/08/20 by J. Socorro, Socorro, J., J. J. Rosales +3 · 1 citation
Physics and Astronomy · #83C20 #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2308.10381
openalex publication_date 2023/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 β=(2α)/(2α- 1). This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when ωX ∈ [0,1], the order belongs to the interval 1≤ β≤ 2, and when ωX∈[-1,0), the order belongs to the interval 0< β≤ 1. In the quantum scheme, we introduce the factor ordering problem in the variables (Ω,ϕ) and its corresponding momenta (ΠΩ, Πϕ), 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(τ), however in the dust era we found a closed solution in the gauge time τ. Keywords: Fractional derivative, Fractional Quantum Cosmology; K-essence formalism; Classical and Quantum exact solutions.