Constructing Covariant Actions for Quantum Gravity with a Unique Vacuum

This paper addresses the ambiguity in the vacuum sector of effective quantum gravity models, which hinders phenomenological investigations. It proposes a constructive framework to formulate 4D covariant actions based on the system's degrees of freedom (dust and gravity) and two guiding principles. This framework leads to a unique and static vacuum solution, resolving the 'curvature polymerisation ambiguity' in loop quantum cosmology and unifying the description of black holes and cosmology.