Massive spin zero fields in cosmology and the tail-free property

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.