Fractional entropy of the Brown-Kucha\v{r} dust in fractional anti-de Sitter quantum gravity

TL;DR

This paper explores the fractional entropy and mass spectrum of Brown-Kuchař dust in anti-de Sitter spacetime using a fractional Wheeler-DeWitt equation, linking fractal properties to quantum gravity effects.

Contribution

It introduces a fractional quantization approach to the Wheeler-DeWitt equation, connecting fractal mass dimensions with fractional quantum operators in AdS quantum gravity.

Findings

Derived the mass spectrum and entropy of Brown-Kuchař dust in AdS.

Established a relationship between fractal mass dimension and fractional quantum parameter.

Proposed implications for fractal cosmic structures in quantum cosmology.

Abstract

This study derives the mass spectrum and entropy of the Brown-Kucha\v{r} 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-Kucha\v{r} dust and L\'evy'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.