Another path for the emergence of modified galactic dynamics from dark matter superfluidity

In recent work we proposed a novel theory of dark matter (DM) superfluidity that matches the successes of the $\mathrm{\Lambda }\mathrm{CDM}$ model on cosmological scales while simultaneously reproducing modified Newtonian dynamics (MOND) phenomenology on galactic scales. The agents responsible for mediating the MONDian force law are superfluid phonons that couple to ordinary (baryonic) matter. In this paper we propose an alternative way for the MOND phenomenon to emerge from DM superfluidity. The central idea is to use higher-gradient corrections in the superfluid effective theory. These next-to-leading order terms involve gradients of the gravitational potential, and therefore effectively modify the gravitational force law. In the process we discover a novel mechanism for generating the nonrelativistic MOND action, starting from a theory that is fully analytic in all field variables. The idea, inspired by the symmetron mechanism, uses the spontaneous breaking of a discrete symmetry. For large acceleration, the symmetry is unbroken and the action reduces to Einstein gravity. For small acceleration, the symmetry is spontaneously broken and the action reduces to MONDian gravity. Cosmologically, however, the Universe is always in the Einstein-gravity, symmetry-restoring phase. The expansion history and linear growth of density perturbations are therefore indistinguishable from $\mathrm{\Lambda }\mathrm{CDM}$ cosmology.

Figure 1

The shaded region corresponds to halos of mass $M$ within which DM forms a superfluid. For a given value of $m$, superfluidity (and along with it the MOND phenomenon) only occurs in sufficiently low-mass halos, where the DM temperature (set by the virial velocity) is below critical. This plot, reproduced from [21], assumes virialization at $z_{\mathrm{vir}}=2$ and treats DM as a free Bose gas.

Figure 2

Numerical solution to the hydrostatic equation (52), which is a MONDian generalization of the Lane-Emden equation, for $n=2$ (solid) and $n=5/2$ (dashed). The boundary conditions are $\mathrm{\Xi }(0)=1$ and ${\mathrm{\Xi }}^{\prime }(0)=0$. The value ${\xi }_1$ at which each solution vanishes, together with the first derivative $\mathrm{d}\mathrm{\Xi }/\mathrm{d}{\xi }_1$ at that point, are listed in Table 1.