Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity

Abstract

This study derives the mass spectrum and entropy of the Brown-Kuchař dust in anti-de Sitter (AdS) spacetime using the fractional Wheeler-DeWitt (WDW) equation. The generalized fractional WDW equation is formulated using a fractional quantization map, demonstrating a correlation between the fractal mass dimension of the Brown-Kuchař dust and Lévy's fractional parameter $\alpha$ of the Riesz fractional quantum operator. These findings may provide new insights into the ramifications of the fractal behavior of cosmic structures in quantum cosmology and quantum gravity.

17 pages, published version

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