Cosmological Weyl-Einsteinian-Cubic Gravity as a gauge theory of gravity

We construct a Weyl-Einsteinian-Cubic Gravity (ECG) as a cubic gauge theory of gravity via abelian gauge and properly tuned compensating real scalar fields. The model is free from any dimensionful parameters. The bare ECG emerges as the lower energy limit of the Weyl-ECG in the local $\textit{non}$-conformal-invariant vacua (i.e., broken phase) in the maximally symmetric spacetimes fixing the vacuum expectation value of the scalar field to the Planck mass scale. Here, the natural presence of (anti-) de Sitter backgrounds spontaneously breaks Weyl's local conformal symmetry akin to the Higgs mechanism, while it is radiatively broken at the renormalization scale at the one-loop level in flat vacua through the Coleman–Weinberg mechanism. The model allows anti-de Sitter and flat spaces but does not allow de Sitter to be vacuum spacetime solutions. The properties of the model deserve further exploration, specifically, those of nonperturbative (e.g., instantons and/or anti-instantons) contributions, for example, in the resurgence or tachyon condensation context requires detailed study.