We consider the renormalization group improvement in the theory of the Standard Model Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. It suggests the range of the Higgs mass 135.6 GeV M H 184.5 GeV compatible with the current CMB data (the lower WMAP bound on n s ), which is close to the widely accepted range dictated by the electroweak vacuum stability and perturbation theory bounds. We find the phenomenon of asymptotic freedom induced by this non-minimal curvature coupling, which brings the theory to the weak coupling domain everywhere except at the lower and upper boundary of this range. The renormalization group running of the basic quantity A I -the anomalous scaling in the non-minimally coupled Standard Model, which analytically determines all characteristics of the CMB spectrum -brings A I to small negative values at the inflation scale. This property is crucial for the above results and may also underlie the formation of initial conditions for the inflationary dynamics in quantum cosmology.

We prove perturbative renormalizability of projectable Hořava gravity. The key element of the argument is the choice of a gauge which ensures the correct anisotropic scaling of the propagators and their uniform falloff at large frequencies and momenta.This guarantees that the counterterms required to absorb the loop divergences are local and marginal or relevant with respect to the anisotropic scaling. Gauge invariance of the counterterms is achieved by making use of the background-covariant formalism. We also comment on the difficulties of this approach when addressing the renormalizability of the non-projectable model.

We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. At the one-loop level with the running of constants taken into account, it leads to a range of the Higgs mass that is entirely determined by the lower WMAP bound on the cosmic microwave background (CMB) spectral index. We find that the SM phenomenology is sensitive to current cosmological data, which suggests to perform more precise CMB measurements as a SM test complementary to the LHC program. By using the concept of a fielddependent cutoff, we show the naturalness of the gradient and curvature expansion in this model within the conventional perturbation theory range of the SM. We also discuss the relation of these results to two-loop calculations and the limitations of the latter caused by parametrization and gauge dependence problems.

1 In contrast to fourth order gravity [15,16], f (R) gravity only propagates the additional "scalaron" [5]. 5 The corresponding projection operators are [Πσ] I J :=σ Iσ J and [Πs] I J = δ I J −σ Iσ J P 1.