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

Abstract

The fractal dimension of large scale galaxy clustering has been reported to be roughlyDF∼2 from a wide range of redshift surveys. If correct, this statistic is of interest for two mainreasons: fractal scaling is an implicit representation of information content, and also thevalue itself is a geometric signature of area. It is proposed that a fractal distribution ofgalaxies may thus be interpreted as a signature of holography (‘fractal holography’),providing more support for current theories of holographic cosmologies. Implications forentropy bounds are addressed. In particular, it is shown that because of spatial scaleinvariance in the matter distribution, violations of the spherical entropy bound can beremoved. This holographic condition instead becomes a rigid constraint on the nature ofthe matter density and distribution in the universe. Inclusion of a dark matter distributionis also discussed, on the basis of theoretical considerations of possible universalΛCDM density profiles.