Abstract
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 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, unless a tuning of the initial values of the running parameters is made. In order to see that this effect may change the predictions we finally include such degree of freedom in the field content and show that Starobinsky's R2 inflation dominates over Higgs inflation.
Highlights
Inflation [1,2,3] is perhaps one of the most natural ways to stretch the initial quantum vacuum fluctuations to the size of the current Hubble patch, seeding the initial perturbations for the cosmic microwave background (CMB) radiation and large scale structure in the universe [4]
We have studied two different aspects of standard Higgs inflation – to seek how fine-tuned the initial conditions should be to fall into a slow-roll attractor solution in an approximate exponentially flat Higgs potential in the Einstein frame
We started with a large kinetic energy, and we found that for an initial kinetic energy density of order 10−3 M P4l the inflaton VEV should be ∼ 10M Pl to sustain inflation long enough to give rise to enough e-folds
Summary
Inflation [1,2,3] is perhaps one of the most natural ways to stretch the initial quantum vacuum fluctuations to the size of the current Hubble patch, seeding the initial perturbations for the cosmic microwave background (CMB) radiation and large scale structure in the universe [4] (for a theoretical treatment, see [5]). The context of extended inflation [10], which has recently received particular attention after the Higgs discovery at the LHC in the context of Higgs inflation [11] By tuning this non-minimal coupling constant, ξ , between the Ricci scalar of the Einstein–Hilbert term and the SM Higgs, it is possible to explain sufficient amount of e-folds of inflation and fit other observables such as the amplitude of temperature anisotropy and the spectral tilt in the CMB data. The inflaton becomes a flat direction, where it does not cost any energy for the field to take any VEV beyond this cut-off Given this constraint on the initial VEV of the inflaton and the new scale, we wish to address two relevant issues concerning the Higgs inflation model [11], one on the classical front and the other on the quantum front. We briefly discuss our results and consequences for inflation in Subsection 4.4, before concluding our paper
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