It is suggested to resolve the contradiction between the two main cosmological observations of the high isotropy of the cosmic microwave background and fractal structure of the large-scale universe by consideration of a hidden support dimension of the multifractal space-luminous distribution of visible matter in the Perseus-Pisces redshift survey. It is shown that while a simple set given by the galaxy space positions has a support dimension $D_0\simeq 2$ inclusion of the galaxy mass (luminosity) leads to a multifractal distribution which can be characterized by two different support dimensions. One of them (corresponding to comparatively rare visible matter) is close to two, whereas the second (corresponding to comparatively dense visible matter) is close to three. The crossover between these two states can be considered as a morphological phase transition.

• Received 28 February 2000

DOI:https://doi.org/10.1103/PhysRevD.62.087303