The selfgravitating gas in the presence of the cosmological constant
Abstract
The nonrelativistic selfgravitating gas in thermal equilibrium in the presence of a positive cosmological constant Λ is investigated. The cosmological constant introduces a force pushing outward all particles with strength proportional to their distance to the center of mass. We consider the statistical mechanics of the selfgravitating gas of N particles in a volume V at thermal equilibrium in the presence of Λ. It is shown that the thermodynamic limit exists and is described by the mean field equations provided N,V→∞ with N/V^{13} fixed andΛV^{23} fixed. That is, Λ→0 for N,V→∞. The case of Λ fixed and N,V→∞ is solved too. We solve numerically the mean field equation for spherical symmetry obtaining an isothermal sphere for Λ>0. The particle distribution becomes flatter when Λ grows compared with the Λ=0 case. Moreover, the particle density increases with the distance when the cosmological constant dominates. There is a bordering case with uniform density. The density contrast between the center and the boundary may be significantly reduced by the cosmological constant. In addition, the critical point associated to the collapse (Jeans') phase transition is pushed towards higher values of N/[TV^{13}] by the presence of Λ>0.
 Publication:

Nuclear Physics B
 Pub Date:
 February 2005
 DOI:
 10.1016/j.nuclphysb.2004.11.013
 arXiv:
 arXiv:astroph/0305322
 Bibcode:
 2005NuPhB.707..529D
 Keywords:

 05.20.y;
 04.40.b;
 64.60.i;
 95.30.Sf;
 Astrophysics;
 Condensed Matter;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 LaTex, 29 pages, 15 .ps figures. Stability analysis revised and improved