On the theory of dark matter superfluidity

Abstract

The ''theory of dark matter superfluidity'' \cite{berezhiani2015theory} is reproduced in SI units with the inclusion of intermediate, and precise, steps in the calculations. By use of another measure of the mean interparticle separation, the bound on dark matter particle mass is less stringent than in \cite{berezhiani2015theory}, though the sub-eV mass range is still found. Using the conjectured superfluid phonon effective field theory, the equation of state is found to be polytropic $P \propto \rho^3$. Due to the increased precision in calculations, the resulting condensate halo radius is found to be less than in \cite{berezhiani2015theory}. The proper acceleration needed is derived in higher precision than in \cite{berezhiani2015theory}, though, when compared to standard gravitational acceleration, is not dominant on large scales $(\sim 100\,\text{kpc})$. Superfluid phonons are generated in galaxies, and breakdown of coherence within the fluid occurs closer to the source than in \cite{berezhiani2015theory}, though dark matter is still found to exist in its normal phase within the Solar System. A relativistic theory that produces proper dynamics in the non-relativistic, weak-field limit is considered, and a starting point for the inclusion of coupling to baryonic matter is suggested. Cosmological dark matter is found in the superfluid state, and the theory is altered to account for this in order to obtain ''cold dark matter'' on these scales. In addition to this, the evolution of the condensate mass density is found to reveal a finite (non-zero) scale factor for which it diverges. Finally, consequences to this theory, mostly considering Bose-Einstein condensate theory, is discussed in short, as well as the same points regarding astrophysics discussed in \cite{berezhiani2015theory}.