Non-topological soliton
The vacuums are separated by the surface of the NTS representing a domain wall configuration (topological defect), which also appears in field theories with broken discrete symmetry.
[1] Infinite domain walls contradict cosmology, but the surface of an NTS is closed and finite, so its existence would not be contradictory.
Quantum field theory has been developed to predict the scattering probability of elementary particles.
that this theory predicts one more class of stable compact objects: non-topological solitons (NTS).
A NTS configuration is the lowest energy solution of classical equations of motion possessing a spherical symmetry.
The spatial size of the NTS configuration may be elementary small or astronomically large, depending on the model fields and constants.
The NTS size could increase with its energy until the gravitation complicates its behavior and finally causes the collapse.
is a constant inside the ball except for a thin surface coat where it sharply drops to the global U(1) symmetrical minimum of
This decay is energetically unprofitable if the sum mass Qm exceed the energy (2).
Q can't exceed N due to the Pauli exclusive principle if the fermions are in the coherent state.
At least two things should be taken into account: (i) the decay into smaller pieces (fission) and (ii) the quantum correction for
Besides, the gauged NTS probably is unstable against a classical decay without conservation of its charge due to complicated vacuum structure of the theory.
symmetric electroweak theory loses its charge (the number of trapped particles) through the neutrino-antineutrino annihilation by emitting photons from the whole volume.
inside Q-star moves from a global maximum of the potential changing the mass of fermions and making them bound.
The described above fermion Q-star has been considered as a model for neutron star[16][17] in the effective hadron field theory.
A complex scalar field could alone form the state of gravitational equilibrium possessing the astronomically large conserved number of particles.
That is more possible for a heavy fermion field: for a such one the energy gain would be the most because it does lose its large mass in the NTS interior, were the Yukawa term
Calculation shows[23] that the NTS solution is energetically favored over a plane wave (free particle) only if
takes into account the charge distribution inside the NTS and the latest one gives the volume vacuum energy.
Nuclei have been considered as NTS's in the effective theory of strong interaction which is easier to deal with than QCD.
, NTS could be simply born as the space became divided onto finite regions of true and false vacuum during the phase transition in the early Universe.
The later are preferable for charged particles to live in due to their smaller masses, so those regions become NTSs.
[25] In case of the second order phase transition as temperature drops below the crucial value
the space consist of interconnecting regions of both false and true vacua with characteristic size
[29] If the field potential allows Q-ball to exist, then they could be born from this condensate as the charge volume density
Breaking the condensate onto Q-balls appears to be favorable over further dilution of the homogeneous charge density by expansion.
[31] Once formed, the NTSs undergo complicated evolution, losing and acquiring the charge by interaction with each other and surrounding particles.
Depending on theory parameters, they could either disappear at all or get statistical equilibrium and "freeze out" at some temperature of the universe, or be born "frozen out" if their interaction is slower than expansion rate at
[32][33] Since an NTS is a composite object, it has to demonstrate properties different from those of a single particle, e.g. evaporation emission, excitation levels, scattering form-factor.
Cosmic observations of such phenomena could provide the unique information about the physics beyond the ability of accelerators.
