  Quantum cosmology is investigated in a de Sitter minisuperspace model with a
quantized scalar field non-minimally coupled to curvature. Quantum states of
the scalar field must satisfy the regularity condition, which requires that the
probability of field fluctuations should not increase with their amplitude. We
show that this condition imposes constraints on the allowed values of the
curvature coupling parameter $\xi$. This is a surprising result, since the
field dynamics depends only on the combination $m^2+\xi R$, where $m$ is the
field mass and $R = \mathrm{const}$ is the curvature, and does not depend on
$\xi$ separately.
