Contents

We explore the possibility that the fundamental theory of nature does not con-tain any scale. This implies a renormalizable quantum gravity theory where the graviton kinetic term has 4 derivatives, and can be reinterpreted as gravity minus an anti-graviton. We compute the super-Planckian RGE of adimensional grav-ity coupled to a generic matter sector. The Planck scale and a flat space can arise dynamically at quantum level provided that a quartic scalar coupling and its β function vanish at the Planck scale. This is how the Higgs boson behaves for Mh ≈ 125 GeV and Mt ≈ 171 GeV. Within agravity, inflation is a generic phe-nomenon: the slow-roll parameters are given by the β-functions of the theory, and are small if couplings are perturbative. The predictions ns ≈ 0.967 and r ≈ 0.13 arise if the inflaton is identified with the Higgs of gravity. Furthermore, quadrati-cally divergent corrections to the Higgs mass vanish: a small weak scale is natura