FIG. 3: Normalized scalar potential of SM inflation in the Einstein frame, in the classical approx- imation (green), or taking into account quantum corrections for m$_{h}$ = 126 . 5 GeV and m$_{h}$ = 128 GeV, in blue and red respectively. Figure is taken from [589]. introduce a dependence of the CMB predictions on the SM particle masses, in particular on the Higgs mass m$_{h}$ and the top quark mass m$_{t}$ as detailed below. The stability of the present classical action could also be affected by the presence of non- renormalizable operators. This represents another serious challenge to the model [290, 590], though this argument can be applied to other high scale models of inflation. Indeed, it is shown that the effective cutoff of the Lagrangian of Eq. (210) is M$_{P}$/ξ , whereas the energy scale of inflation is M$_{P}$$_{/}$√$_{ξ}$$_{. One therefore should expect non-renormalizable contributions}$ to the action to be relevant at energies well below inflation. This represents a challenge to the model since the implicit assumption is that the SM of particle physics is the effective theory at least up to the inflationary scale. In the absence of symmetries to prevent the appearance of non-renormalizable contributions the model should be considered as fine-tuned, so that these contributions do not spoil the flatness of the model. 2. SM Higgs inflation and implications for collider experiments As mentioned above, the important feature of this model of inflation is that masses of SM particles enter the quantum corrections to the scalar potential, and thus impact the CMB predictions n$_{s}$ , r and α$_{s}$ . In particular the most important masses that affect the 97