Creation of the universe with a stealth scalar field

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.