  In recent work we proposed a novel theory of dark matter (DM) superfluidity
that matches the successes of the LambdaCDM 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 non-relativistic 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
LambdaCDM cosmology.
