Condensation of charged bosons in plasma physics and cosmology

We consider the screening of impurities in plasma with a Bose–Einstein condensate of electrically charged bosons and show that the screened potential is drastically different from the usual Debye potential. The polarization operator of photons in plasma acquires infrared singular terms at small photon momentum, and the screened potential drops down as a power of distance and even has an oscillating behavior, similar to the Friedel oscillations in plasma with degenerate fermions. We also discuss the magnetic properties of the cosmological plasma with condensed $W$ bosons and show that $W$ bosons condense in the ferromagnetic state. This could lead to spontaneous magnetization of the primeval plasma. The created magnetic fields may seed galactic and intergalactic magnetic fields observed in the present-day Universe.