We extract from data the parameters of the Higgs potential, the top Yukawa coupling and the electroweak gauge couplings with full 2-loop NNLO precision, and we extrapolate the SM parameters up to large energies with full 3-loop NNLO RGE precision. Then we study the phase diagram of the Standard Model in terms of high-energy parameters, finding that the measured Higgs mass roughly corresponds to the minimum values of the Higgs quartic and top Yukawa and the maximum value of the gauge couplings allowed by vacuum metastability. We discuss various theoretical interpretations of the near-criticality of the Higgs mass.

We explore the possibility that the fundamental theory of nature does not contain 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 gravity 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 M _h ≈ 125 GeV and M _t ≈ 171 GeV. Within agravity, inflation is a generic phenomenon: the slow-roll parameters are given by the β-functions of the theory, and are small if couplings are perturbative. The predictions n _s ≈ 0.967 and r ≈ 0.13 arise if the inflaton is identified with the Higgs of gravity. Furthermore, quadratically divergent corrections to the Higgs mass vanish: a small weak scale is natural and can be generated by agravity quantum corrections.

Theories where the Planck scale is dynamically generated from dimensionless interactions provide predictive inflationary potentials and super-Planckian field variations. We first study the minimal single field realisation in the low-energy effective field theory limit, finding the predictions n_s ≈ 0.96 for the spectral index and r ≈ 0.13 for the tensor-to-scalar ratio, which can be reduced down to ≈ 0.04 in presence of large couplings. Next we consider agravity as a dimensionless quantum gravity theory finding a multifield inflation that converges towards an attractor trajectory and predicts n_s ≈ 0.96 and 0.003 < r < 0.13, interpolating between the quadratic and Starobinsky inflation. These theories relate the smallness of the weak scale to the smallness of inflationary perturbations: both arise naturally because of small couplings, implying a reheating temperature of 10⁷⁻⁹ GeV. A measurement of r by Keck/Bicep3 would give us information on quantum gravity in the dimensionless scenario.

We investigate whether Higgs inflation can occur in the Standard Model starting from natural initial conditions or not. The Higgs has a non-minimal coupling to the Ricci scalar. We confine our attention to the regime where quantum Einstein gravity effects are small in order to have results that are independent of the ultraviolet completion of gravity. At the classical level we find no tuning is required to have a successful Higgs inflation, provided the initial homogeneity condition is satisfied. On the other hand, at the quantum level we obtain that the renormalization for large non-minimal coupling requires an additional degree of freedom that transforms Higgs inflation into Starobinsky $R^2$ inflation, unless a tuning of the initial values of the running parameters is made

Adding the terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory (QFT). The price to pay is a massive ghost, which is due to the higher derivatives that the terms quadratic in the curvature imply. In this paper, the quadratic gravity scenario is reviewed including the recent progress on the related stability problem of higher derivative theories. The renormalization of the theory is also reviewed and the final form of the full renormalization group equations in the presence of a generic renormalizable QFT is presented. The theory can be extrapolated up to infinite energy through the renormalization group if all matter couplings flow to a fixed point (either trivial or interacting). Moreover, besides reviewing the above-mentioned topics, are some further insight on the ghost issue and the infinite energy extrapolation are provided. There is hope that in the future, this scenario might provide a phenomenologically viable and UV complete relativistic field theory of all interactions.