Abstract
The present paper may conditionally be divided into three tightly associated parts. The first part is a discussion of the necessity of conformal covariance of the general relativistic scalar field equation following from quantum field theory. The second part is an objection against the assertion or implication in Reps. [3, 5] that in the De Sitter world (and as a consequence, in some other cosmological models) the rest mass of the scalar particle cannot be zero. In the third part the forbiddenness of the cubic self-interaction of the scalar field vs. the quartic one in cosmological models under consideration is shown. This forbiddenness manifests in that there exist divergences of a special type (not ultraviolet) in perturbation theory for the former interaction, but there is no such divergence for the latter. The relation of the results with the reality is discussed.
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