Comment on "Scalar Einstein-Aether theory"

A recent paper studies a modification of Einstein-aether theory in which the aether vector is restricted, at the level of the action, to be the gradient of a scalar. In this comment we note that this scalar version of Einstein-aether theory is equivalent to the projectable version of the IR limit of Ho\v{r}ava gravity when the potential for the scalar is constant. This provides a generally covariant formulation for projectable Ho\v{r}ava gravity.