Astron. Astrophys. 344, 27-35 (1999)

Dynamical scaling of matter density correlations in the Universe

An application of the dynamical renormalization group

A. Domínguez ¹, D. Hochberg ¹, J.M. Martín-García ¹, J. Pérez-Mercader ¹ and L.S. Schulman <sup>2

1</sup> Laboratorio de Astrofísica Espacial y Física Fundamental (INTA-CSIC), Apartado 50727, E-28080 Madrid, Spain
² Department of Physics, Clarkson University, Potsdam, New York 13699-5820, USA

Received 9 July 1998 / Accepted 15 December 1998

Abstract

We show how the interplay of non-linear dynamics, self-gravity, and fluctuations leads to self-affine behavior of matter density correlations quite generically, i.e., with a power law exponent whose value does not depend in a very direct way on the specific details of the dynamics. This we do by means of the Renormalization Group, a powerful analytical tool for extracting asymptotic behavior of many-body systems.

Key words: gravitation hydrodynamics methods: analytical cosmology: theory cosmology: large-scale structure of Universe

Send offprint requests to: D. Hochberg (hochberg@laeff.esa.es)

This article contains no SIMBAD objects.

Contents

• 1. Introduction
• 2. From hydrodynamics to the KPZ equation
• 3. Adiabatic approximation
• 4. The renormalization group equations
  • 4.1. Calculation of the RGEs
• 5. Fixed points
  • 5.1. The value of the critical exponents at each critical point. White noise
  • 5.2. The value of the critical exponents at each critical point. Colored noise
• 6. Scaling properties of matter density correlations
• 7. Discussion and conclusions
• Acknowledgements
• References

© European Southern Observatory (ESO) 1999

Online publication: March 10, 1999
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