Fractal cosmology in an open universe

¹ Dipartimento di Fisica, Università di Roma “La Sapienza” - I-00185 Roma, Italy
² INFN, Sezione di Roma I - I-00185 Roma, Italy
³ INFM Sezione Roma I - I-00185 Roma, Italy
⁴ Joseph Henry Laboratories, Princeton University - Princeton, NJ 08544, USA
⁵ Département de Physique Théorique, Université de Genève CH-1211 Genève, Switzerland

Received: 4 October 1999
Accepted: 22 February 2000

Abstract

The clustering of galaxies is well characterized by fractal properties, with the presence of an eventual cross-over to homogeneity still a matter of considerable debate. In this letter we discuss the cosmological implications of a fractal distribution of matter, with a possible cross-over to homogeneity at an undetermined scale . Contrary to what is generally assumed, we show that, even when , this possibility can be treated consistently within the framework of the expanding universe solutions of Friedmann. The fractal is a perturbation to an open cosmology in which the leading homogeneous component is the cosmic background radiation (CBR). This cosmology, inspired by the observed galaxy distributions, provides a simple explanation for the recent data which indicate the absence of deceleration in the expansion (). Correspondingly the “age problem” is also resolved. Further we show that the model can be extended back from the curvature-dominated arbitrarily deep into the radiation-dominated era, and we discuss qualitatively the modifications to the physics of the anisotropy of the CBR, nucleosynthesis and structure formation.