## Force equation of the large-scale structure of the Universe
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.
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
- 4. A force equation for homogeneous, isotropic distributions in Boltzmann equilibrium
- 5. Newtonian interaction and expansion
- 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 |