Moving superfluids in the rotating universe

Abstract 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.