Agravity up to infinite energy

The self-interactions of the conformal mode of the graviton are controlled, in dimensionless gravity theories (agravity), by a coupling $f_0$ that is not asymptotically free. We show that, nevertheless, agravity can be a complete theory valid up to infinite energy. When $f_0$ grows to large values, the conformal mode of the graviton decouples from the rest of the theory and does not hit any Landau pole provided that scalars are asymptotically conformally coupled and all other couplings approach fixed points. Then agravity can flow to conformal gravity at infinite energy. We identify scenarios where the Higgs mass does not receive unnaturally large physical corrections. We also show a useful equivalence between agravity and conformal gravity plus two extra conformally coupled scalars, and we give a simpler form for the renormalization group equations of dimensionless couplings as well as of massive parameters in the presence of the most general matter sector.