  We present a complete study of a family of tachyonic scalar fields living on
the de Sitter universe. We show that for an infinite set of discrete values of
the negative squared mass the fields exhibit a gauge symmetry and there exists
for them a fully acceptable local and covariant quantization similar to the
Feynman-Gupta-Bleuler quantization of free QED. For general negative squares
masses we also construct positive quantization where the de Sitter symmetry is
spontaneously broken. We discuss the sense in which the two quantizations may
be considered physically inequivalent even when there is a Lorentz invariant
subspace in the second one.
