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

The fractal dimension of large scale galaxy clustering has been reported to be roughly D-F similar to 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 a 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, it is shown that because of spatial scale invariance in the matter distribution, 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, on the basis of theoretical considerations of possible universal CDM density profiles.