Scale Symmetry in the Universe

Abstract

Scale symmetry is a fundamental symmetry of physics that seems however not to be fully realized in the universe. Here, we focus on the astronomical scales ruled by gravity, where scale symmetry holds and gives rise to a truly scale invariant distribution of matter, namely it gives rise to a fractal geometry. A suitable explanation of the features of the fractal cosmic mass distribution is provided by the nonlinear Poisson--Boltzmann--Emden equation. An alternative interpretation of this equation is connected with theories of quantum gravity. We study the fractal solutions of the equation and connect them with the statistical theory of random multiplicative cascades, which originated in the theory of fluid turbulence. The type of multifractal mass distributions so obtained agrees with results from the analysis of cosmological simulations and of observations of the galaxy distribution.

19 pages, 5 figures

References in corpus (4)

• Halos and voids in a multifractal model of cosmic structure
• The Fractal Geometry of the Cosmic Web and its Formation
• Dynamics and thermodynamics of systems with long-range interactions: interpretation of the different functionals
• Fractal analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey