Higgs and gravitational scalar fields together induce Weyl gauge

Understand

A common biquadratic potential for the Higgs field $h$ and an additional scalar field $\phi$, non minimally coupled to gravity, is considered in locally scale symmetric approaches to standard model fields in curved spacetime.

• A common ground state of the two scalar fields exists and couples both fields to gravity, more precisely to scalar curvature $R$.
• In Einstein gauge ($\phi = const$, often called "Einstein frame"), also $R$ is scaled to a constant.
• This condition makes perfect sense, even in the general case, in the Weyl geometric approach.