Acausality in Superfluid Dark Matter and MOND-like Theories

TL;DR

This paper investigates the causality and locality properties of superfluid dark matter models that aim to replicate MOND-like galactic phenomenology, revealing issues with superluminality and non-locality in their theoretical frameworks.

Contribution

It analyzes the high-energy behavior of superfluid dark matter models and related theories, highlighting fundamental causality and locality challenges.

Findings

High-energy perturbations violate hyperbolicity in superfluid models.

Models exhibit superluminal propagation in certain phase space regions.

Alternative models also show non-locality issues.

Abstract

There has been much interest in novel models of dark matter that exhibit interesting behavior on galactic scales. A primary motivation is the observed Baryonic Tully-Fisher Relation in which the mass of galaxies increases as the quartic power of rotation speed. This scaling is not obviously accounted for by standard cold dark matter. This has prompted the development of dark matter models that exhibit some form of so-called MONDian phenomenology to account for this galactic scaling, while also recovering the success of cold dark matter on large scales. A beautiful example of this are the so-called superfluid dark matter models, in which a complex bosonic field undergoes spontaneous symmetry breaking on galactic scales, entering a superfluid phase with a 3/2 kinetic scaling in the low energy effective theory, that mediates a long-ranged MONDian force. In this work we examine the causality and locality properties of these and other related models. We show that the Lorentz invariant completions of the superfluid models exhibit high energy perturbations that violate global hyperbolicity of the equations of motion in the MOND regime and can be superluminal in other parts of phase space. We also examine a range of alternate models, finding that they also exhibit forms of non-locality.