Ponderable aether

Abstract

We consider a Lorentz-violating theory of gravity where the aether vector is taken to be nondynamical. This "ponderable aether theory" is almost the same as Einstein-aether theory (where the aether vector is dynamical), but involves additional integration constants arising due to the loss of initial value constraints. One of these produces an effective energy density for the aether fluid, similar to the appearance of dark matter in projectable Ho\v{r}ava gravity and the mimetic dark matter theory. Here we investigate the extent to which this energy density can reproduce the phenomenology of dark matter. Although it is indistinguishable from cold dark matter in homogeneous, isotropic cosmology, it encounters phenomenological problems in both spherically symmetric configurations and cosmological perturbations. Furthermore, inflationary considerations lead us to expect a tiny value for the ponderable aether energy density today unless a sourcing effect is added to the theory. The theory then effectively reduces to dynamical Einstein-aether theory, rendering moot the question of whether an aether must be dynamical in order to be consistent.