Propagation of massless scalar field in standard-like cosmological models

The propagation of the massless scalar waves in Robertson-Walker space-time s does not lie, in general, on the light cones and is very sensible to the underlying cosmological time evolution. This can be put in particular evide nce for a class of Robertson-Walker space-times by means of the previously determined explicit solutions of the corresponding massless generalized Kle in-Gordon equation. A simple condition on the parameters of the cosmologica l model (that is satisfied in Standard Cosmology) is determined such that t he massless scalar field has a tail-free propagation, that is it entirely p ropagates on the light cones. The property is proved for a countable set of values of the coupling constant between the scalar field and the gravitati onal field that includes the minimally and the conformally coupled case.