On the de Sitter Tardyons and Tachyons

TL;DR

This paper demonstrates that classical tachyons cannot exist on de Sitter manifolds due to geodesic restrictions, while quantum scalar tachyons remain well-defined and free of such limitations in this geometry.

Contribution

It provides a detailed analysis of classical versus quantum tachyons on de Sitter manifolds, showing classical restrictions and quantum consistency.

Findings

Classical tachyons are restricted and cannot exist on de Sitter manifolds.

Quantum scalar tachyons are well-defined and behave as tempered distributions.

Tachyonic scalar and Dirac plane waves are explicitly constructed in this geometry.

Abstract

It is shown that on the de Sitter manifolds the tachyonic geodesics are restricted such that the classical tachyons cannot exist on this manifold at any time. On the contrary, the theory of the scalar quantum tachyons is free of any restriction. The tachyonic scalar and Dirac plane waves are deduced in this geometry, pointing out that these are well-defined, behaving as tempered distributions at any moment.