Safe essential scalar-tensor theories

Understand

We discuss the renormalisation group flow of all essential couplings of quantum gravity coupled to a shift-symmetric scalar field at fourth order in the derivative expansion.

• We derive the global structure of the phase diagram, and identify a bounded region in theory space which is both asymptotically safe in the ultraviolet, and connects to standard effective field theory in the infrared.
• Our system thus satisfies the weak-gravity bound.
• The allowed infrared behaviour of the essential four-scalar coupling is restricted by requiring an ultraviolet completion.