Mechanics and kinetics in the Friedmann-Lemaitre-Robertson-Walker space-times

TL;DR

This paper develops the mechanics and kinetic equations in FLRW space-times using canonical formalism, deriving transformation laws, invariance properties, and solutions to the collisionless Boltzmann equation relevant for cosmological models.

Contribution

It introduces a canonical formalism approach to mechanics and kinetics in FLRW space-times, including transformation laws and explicit solutions to the Boltzmann equation.

Findings

Derived equations of mechanics and kinetics in FLRW space-times.

Found the transformation law of generalized momentum under coordinate shifts.

Obtained solutions to the collisionless Boltzmann equation for homogeneous distributions.

Abstract

Using the standard canonical formalism, the equations of mechanics and kinetics in the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-times in Cartesian coordinates have been obtained. The transformation law of the generalized momentum under the shift of the origin of the coordinate system has been found, and the form invariance of the Hamiltonian function relative to the shift transformation has been proved. The general solution of the collisionless Boltzmann equation has been found. In the case of the homogeneous distribution the solutions of the kinetic equation for several simple, but important for applications, cases have been obtained.