Fractal dust model of the Universe based on Mandelbrot's Conditional Cosmological Principle and General Theory of Relativity

摘要

We present a fractal dust model of the Universe based on Mandelbrot'sproposal to replace the standard Cosmological Principle by his ConditionalCosmological Principle within the framework of General Theory of Relativity.This model turns out to be free from the de-Vaucouleurs paradox and isconsistent with the SNe1a observations. The expected galaxy count as a functionof red-shift is obtained for this model. An interesting variation is a steadystate version, which can account for an accelerating scale factor without anycosmological constant in the model.