  The spontaneous breaking of an approximate discrete symmetry is considered,
with the resulting protodomains of true and false vacuum being separated by
domain walls. Given a strong, symmetric Yukawa coupling of the real scalar
field to a generic fermion, the domain walls accumulate a gas of fermions,
which modify the domain wall dynamics. The splitting of the degeneracy of the
ground states results in the false vacuum protodomain structures eventually
being fragmented into tiny false vacuum bags with a Fermi gas shell (Fermi
balls), that may be cosmologically stable due to the Fermi gas pressure and
wall curvature forces, acting on the domain walls. As fermions inhabiting the
domain walls do not undergo number density freeze out, stable Fermi balls exist
only if a fermion anti-fermion asymmetry occurs. Fermi balls formed with a new
Dirac fermion that possesses no standard model gauge charges provide a novel
cold dark matter candidate.
