Astron. Astrophys. 326, 433-441 (1997)

Force equation of the large-scale structure of the Universe

Martín López-Corredoira

Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Spain

Received 27 August 1996 / Accepted 20 May 1997

Abstract

This article presents a statistical-mechanical treatment of a relationship (the force equation) between the gravitational potential for two particles and the correlation functions in a relaxed distribution of particles with different masses. This relationship is used in the case of galaxies interacting through a Newtonian potential in a Universe in expansion, i.e. the large-scale distribution of galaxies.

By applying this equation and from the observed two-point correlation function for galaxies as a -1.8 exponent power law, I derive the approximate dependence of a mass-mass correlation function as a -2.8 exponent power law, i.e. I infer that mass is more correlated than galaxies at short distances, when the distribution is considered as relaxed.

Key words: gravitation dark matter large-scale structure of Universe

Send offprint requests to: martinlc@iac.es

Contents

• 1. Introduction
• 2. The probability of mass and position for a particle with a known mass function distribution and Boltzmann equilibrium.
  • 2.1. Probability of positions
  • 2.2. Probability of masses
  • 2.3. Normalized probability
• 3. Correlation functions
  • 3.1. Particle-particle two-point correlation function
  • 3.2. Mass-mass two-point correlation function
  • 3.3. Mass-particle two-point correlation function
  • 3.4. Mass-mass-particle three-point correlation function
• 4. A force equation for homogeneous, isotropic distributions in Boltzmann equilibrium
• 5. Newtonian interaction and expansion
  • 5.1. Newtonian interaction
  • 5.2. Effects of the expansion of the Universe
• 6. The meaning of
• 7. How to obtain the correlations from the distribution
• 8. Application on the Large-scale distribution of galaxies
• 9. Results, other applications and further commentaries
• Acknowledgements
• References

© European Southern Observatory (ESO) 1997

Online publication: October 15, 1997
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