  If textbook Lorentz invariance is actually a property of the equations
describing a sector of the excitations of vacuum above some critical distance
scale, several sectors of matter with different critical speeds in vacuum can
coexist and an absolute rest frame (the vacuum rest frame) may exist without
contradicting the apparent Lorentz invariance felt by "ordinary" particles
(particles with critical speed in vacuum equal to $c$ , the speed of light).
The sectorial Lorentz symmetry may be only a low-energy limit, in the same way
as the relation $\omega $ (frequency) = $c_s$ (speed of sound) $k$ (wave
vector) holds for low-energy phonons in a crystal. We study the consequences of
such a scenario, using an ansatz inspired by the Bravais lattice as a model for
some vacuum properties. It then turns out that: a) the Greisen-Zatsepin-Kuzmin
cutoff on high-energy cosmic protons and nuclei does no longer apply; b)
high-momentum unstable particles have longer lifetimes than expected with exact
Lorentz invariance, and may even become stable at the highest observed cosmic
ray energies or slightly above. Some cosmological implications of superluminal
particles are also discussed.
