The Statistical Model with Interpartial Scalar Conformally Invariant Interaction

TL;DR

This paper develops a mathematical model for a self-gravitating scalar charged particle system with conformal invariance, analyzing its properties in ultrarelativistic and early universe conditions.

Contribution

It introduces a new statistical model incorporating conformal invariance for scalar interactions in a gravitational context, with analysis of asymptotic behaviors.

Findings

Scalar charge density generates scalar field effective mass.

The model exhibits asymptotic conformal invariance in a homogeneous isotropic universe.

Effective mass of scalar field is explicitly calculated.

Abstract

A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic properties of the model are investigated in the ultrarelativistic limit. It is shown, that scalar charge density automatically generates scalar field effective mass and the value of this mass is found. In the paper it is proved the asymptotic conformal invariance of constitutive equations in case of homogenous isotropic Universe. Also it is proved the asymptotic conformal invariance of field equations at the early stages of cosmological evolution.