  Fields of spin $s \geq 1/2$ satisfying wave equations in a curved space obey
the Huygens principle under certain conditions clarified by a known theorem.
Here this theorem is generalized to spin zero and applied to an inflaton field
in de Sitter-like space, showing that tails of scalar radiation are an
unavoidable physical feature. Requiring the absence of tails, on the contrary,
necessarily implies an unnatural tuning between cosmological constant, scalar
field mass, and coupling constant to the curvature.
