Topological quantum correction to an atomic ideal gas law as a dark
  energy effect
  The traditional ambiguity about the bulk electrostatic potentials in crystals
is due to the conditional convergence of Coulomb series. The classical Ewald
approach turns out to be the first one resolving this task as consistent with a
translational symmetry. The latter result appears to be directly associated
with the thermodynamic limit in crystals. In this case the solution can also be
obtained upon direct lattice summation, but after subtracting the mean Bethe
potential. As shown, this effect is associated with special periodic boundary
conditions at infinity so as to neutralize an arbitrary choice of the unit-cell
charge distribution. However, the fact that any additional potential exerted by
some charge distribution must in turn affect that charge distribution in
equilibrium is not discussed in the case at hand so far. Here we show that in
the simplest event of gaseous atomic hydrogen as an example, the
self-consistent mean-field-potential correction results in an additional
pressure contribution to an ideal gas law. As a result, the corresponding
correction to the sound velocity arises. Moreover, if gas in question is not
bounded by any fixed volume, then some acceleration within that medium is
expected. Addressed to the Friedman hypersphere, our result may be interesting
in connection with the accelerating Universe revealed experimentally and
discussed intensively.
