de Sitter Tachyons and Related Topics

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.