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.
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