In flat AdS quantum cosmology with Brown-Kuchar dust, the fractional Wheeler-DeWitt equation yields mass and entropy spectra scaling as (n+1/2)^(alpha/2), with a fractal mass dimension D = 3 alpha / 2.
The Fractal Geometry of the Cosmic Web and its Formation
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abstract
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body simulations or the Sloan Digital Sky Survey are elucidated by means of multifractal geometry. A non-lacunar multifractal geometry can encompass three fundamental descriptions of the cosmic structure, namely, the web structure, hierarchical clustering, and halo distributions. Furthermore, it explains our present knowledge of cosmic voids. In this way, a unified theory of the large-scale structure of the universe seems to emerge. The multifractal spectrum that we obtain significantly differs from the one of the adhesion model and conforms better to the laws of gravity. The formation of the cosmic web is best modeled as a type of turbulent dynamics, generalizing the known methods of Burgers turbulence.
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Fractional entropy of the Brown-Kucha\v{r} dust in fractional anti-de Sitter quantum gravity
In flat AdS quantum cosmology with Brown-Kuchar dust, the fractional Wheeler-DeWitt equation yields mass and entropy spectra scaling as (n+1/2)^(alpha/2), with a fractal mass dimension D = 3 alpha / 2.