The stability of galaxies in an expanding Universe obtained by Newtonian dynamics

The dynamics of galaxies in an expanding Universe is often determined for
gravitational and dark matter in an Einstein-de Sitter Universe, or alternatively
by modifying the gravitational long-range attractions in the Newtonian dynamics. Here the time evolution of galaxies is determined by simulations of systems
with pure gravitational forces by classical molecular dynamic simulations. A
time reversible algorithm for formation and aging of gravitational systems by
self-assembly of baryonic objects, recently derived (Toxvaerd 2022 Eur. Phys.
J. Plus 137 99), is extended to include the Hubble expansion of the space.
The algorithm is stable for billions of time steps without any adjustments. The
algorithm is used to simulate simple models of the Milky Way with the Hubble
expansion of the Universe, and the galaxies are simulated for times which
corresponds to more than 25 Gyr. The rotating galaxies lose bound objects
from time to time, but they are still stable at the end of the simulations. The
simulations indicate that the explanation for the dynamics of galaxies may be
that the Universe is very young in cosmological times. Although the models
of the Milky Way are rather stable at 13–14 Gyr, which corresponds to the
cosmological time of the Universe, the Hubble expansion will sooner or later
release the objects in the galaxies. But the simulations indicate that this will
first happen in a far away future.