  The stealth scalar field is a non-trivial configuration without any
back-reaction to geometry, which is characteristic for non-minimally coupled
scalar fields. Studying the creation probability of the de Sitter universe with
a stealth scalar field by the Hartle and Hawking's semi-classical method, we
show that the effect of the stealth field can be significant. For the class of
scalar fields we consider, creation with a stealth field is possible for a
discrete value of the coupling constant and its creation probability is always
less than that with a trivial scalar field. However, those creation rates can
be almost the same depending on the parameters of the theory.
