  The possibility that Lorentz symmetry is violated in gravitational processes
is relatively unconstrained by experiment, in stark contrast with the level of
accuracy to which Lorentz symmetry has been confirmed in the matter sector. One
model of Lorentz violation in the gravitational sector is Einstein-aether
theory, in which Lorentz symmetry is broken by giving a vacuum expectation
value to a dynamical vector field. In this paper we analyse the effective
theory for quantised gravitational and aether perturbations. We show that this
theory possesses a controlled effective expansion within dimensional
regularisation, that is, for any process there are a finite number of Feynman
diagrams which will contribute to a given order of accuracy. We find that there
is no log-running of the two-derivative phenomenological parameters, justifying
the use of experimental constraints for these parameters obtained over many
orders of magnitude in energy scale. Given the stringent experimental bounds on
two-derivative Lorentz-violating operators, we estimate the size of matter
Lorentz-violation which arises due to loop effects. This amounts to an
estimation of the natural size of coefficients for Lorentz-violating
dimension-six matter operators, which in turn can be used to obtain a new bound
on the two-derivative parameters of this theory.
