A new scale in the quasi-static limit of Aether Scalar Tensor Theory (2305.07742v3)

Abstract: One of the aims of Aether Scalar Tensor Theory (AeST) is to reproduce the successes of Modified Newtonian Dynamics (MOND) on galactic scales. Indeed, the quasi-static limit of AeST achieves precisely this, assuming that the vector field $\vec{A}$ vanishes and that the so-called ghost condensate can be neglected. The effects of the ghost condensate were investigated in detail in previous studies. Here, we focus on the assumption of a vanishing vector field. We argue that this assumption is not always justified and show how to correctly take into account the vector field, finding that the quasi-static limit depends on a model parameter $m_\times$. In the limit $m_\times \to 0$, one recovers the quasi-static limit with a vanishing vector field. In particular, one finds a two-field version of MOND. In the opposite limit, $m_\times \to \infty$, one finds a single-field version of MOND. We show that, in practice, much of the phenomenology of the quasi-static limit depends only very little on the value of $m_\times$. Still, for some observational tests, such as those involving wide binaries, $m_\times$ has percent-level effects that may be important.