Moving superfluids in the rotating universe

We study homogeneous cosmological models featuring shift-symmetric scalar fields (or, superfluids) in relative motion. In the presence of anisotropy this universe generally features rotation, in the sense that the principal axes of anisotropic expansion rotate with respect to the cosmic comoving frame. We focus in particular on the minimal case of two superfluids in 2+1 dimensions. The momentum constraint enforces their spatial gradients to be collinear and the dynamics tends to align such a direction with that of maximal expansion at late times. As opposed to the recently studied case of solids, rotation plays a more important role in the present two-superfluids model. The associated energy density does not dilute away but scales as that of anisotropy and affects the total equation of state. We find that purely non-rotating solutions correspond to an unstable surface in phase space in the direction of non-vanishing rotation. This suggests that rotation is a crucial feature of these scenarios that cannot be neglected.