Abstract
In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. Initially, we find that electroweak scale measurements may be dissonant to the limits obtained from the cosmological data sets used in the analysis. Specifically, an ≈ 8σ-discrepancy between the inflationary parameters and the value of the Monte Carlo reconstructed top quark mass is found. However, considering the most recent results obtained by the CMS Collaboration from differential cross-section measurements of the top quark production a good agreement is obtained.
Highlights
The Renormalization Group Equations (RGE) of the SM couplings one obtains that the Higgs quartic coupling evolve to small negative values [22,23,24,25,26], which amounts to saying that the SM develops an unstable scalar potential for energy scales larger than a critical value around 1010 − 1011 GeV
Considering the inherent theoretical uncertainties to the definition of the top quark Yukawa coupling from the Monte Carlo reconstruction of the top quark mass [33], one is able to show the stability of the standard model vacuum state within 2σ deviation [34]
We solve the two-loop Renormalization Group Equations (RGE) for the SM parameters to obtain the corresponding constraints at the electroweak scale and the upper limit to the top quark pole mass, in order to examine if current cosmological data are compatible with the electroweak phenomenology and the inflationary dynamics of the Higgs field
Summary
Before considering the Higgs Inflation mechanism, let’s discuss the effective potential of the Standard Model minimally coupled to gravity. The one-loop contributions to the effective coupling recover the structure derived by Coleman and Weinberg [43], λ(1)(μ). As discussed in [24, 25, 49, 50], the Higgs quartic coupling λ and its β-function βλ run to small values, reaching a minimum somewhere bellow the Planck scale. This suggests that λ, as well as its β-function, holds only a weak dependence with the renormalization scale μ. The problem with large-logarithms is avoided as long as βλ(M )/4 ln (h/M ) 1
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