Fractal Holography: a geometric re-interpretation of cosmological large scale structure

TL;DR

This paper proposes that the fractal distribution of galaxies, with a dimension around 2, can be interpreted as a signature of holography, offering insights into cosmological entropy bounds and matter distribution.

Contribution

It introduces the concept of fractal holography, linking galaxy clustering fractal dimensions to holographic principles in cosmology, and discusses implications for entropy bounds and dark matter.

Findings

Fractal dimension of galaxy clustering is approximately 2.

Holographic interpretation constrains matter density and distribution.

Violations of entropy bounds can be addressed through scale invariance.

Abstract

The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit representation of information content, and also the value itself is a geometric signature of area. It is proposed that the fractal distribution of galaxies may thus be interpreted as a signature of holography (``fractal holography''), providing more support for current theories of holographic cosmologies. Implications for entropy bounds are addressed. In particular, because of spatial scale invariance in the matter distribution, it is shown that violations of the spherical entropy bound can be removed. This holographic condition instead becomes a rigid constraint on the nature of the matter density and distribution in the Universe. Inclusion of a dark matter distribution is also discussed, based on theoretical considerations of possible universal CDM density profiles.