  Models with extra space-time dimensions produce, tipically, a 4D effective
theory whose vacuum is not exactly Lorentz invariant but can be considered a
physical medium whose refractive index is determined by the gravitational
field. This leads to a version of relativity with a preferred frame and to look
for experimental tests with the new generation of ether-drift experiments using
rotating cryogenic optical resonators. Considering various types of cosmic
motion, we formulate precise predictions for the modulations of the signal
induced by the Earth's rotation and its orbital revolution around the Sun. We
also compare with recent experimental results that might represent the first
modern experimental evidence for a preferred frame.
