Three problems of superfluid dark matter and their solution

Abstract

In superfluid dark matter (SFDM), the phonon field plays a double role: It carries the superfluid's energy density and it mediates the MOND-like phonon force. We show that these two roles are in tension with each other on galactic scales: A MOND-like phonon force is in tension with a superfluid in equilibrium and with a significant superfluid energy density. To avoid these tensions, we propose a model where the two roles are split between two different fields. This also allows us to solve a stability problem in a more elegant way than standard SFDM. We argue that the standard estimates for the size of a galaxy's superfluid core need to be revisited.

Acausality in Superfluid Dark Matter and MOND-like Theories

“…Finally, we mention an attempt to reconcile what Ref. [47] describes as a tension between a superfluid in equilibrium and a significant superfluid energy density by splitting these two roles between two different fields. This paper studied another K-essence theory of the form…”

“…In Ref. [47] the focus was on ensuring the sound speeds were subluminal, but this is only one requirement for consistency. The more general requirement is that high energy particles exhibit subluminality too; we shall return to this discussion in Section VII C. When we substitute Eq.…”

“…Only θ + is coupled to baryonic matter σ B , separating these two roles of the superfluid (we note that the energy density σ B is not Lorentz invariant, but it was the choice of Ref. [47]). By perturbing around a background solution, the sound speed of θ + propagations were found to be superluminal,…”

“…Ref. [47] includes an appendix which describes a way to lift Eq. (98) to a smooth Lagrangian, but the form of the theory arrived at by this process is simply of the form of a multi-field version of Eq.…”