On Higgs inflation and naturalness

Abstract

We reexamine recent claims that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Λ ≃ M p /ξ. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.

Higgs inflation as a mirage

“…In our case, however, the extra term modifies this behaviour, leading to the simpler relation: 8) with the potential going as 9) in the asymptotic region. The inflationary predictions are obviously affected.…”

“…When analyzed near the SM vacuum, the operator (1.1) has dimension five by power counting, with an effective cutoff scale Λ ≡ M p ξ , well below the edge of the plateau [7,8,10]. 1 In a traditional effective field theory interpretation, the operator (1.1) would arise from integrating out heavy degrees of freedom, to be found below the scale Λ.…”

“…Although such metastability is mild and the lifetime of the vacuum is extremely large compared with the age of the Universe, the viability of Higgs inflation does require a positive potential at large field values. 8 However, stability of the potential at large scales requires experimentally disfavored values of m t and/or m h (even allowing for a larger error in the determination of m t [17]) disfavoring also the possibility of Higgs inflation [18]. A simple, generic and very efficient cure of the potential instability was proposed in ref.…”

“…In the low-energy effective theory the Higgs mass looks dangerously light for stability, but the UV-complete theory above the singlet threshold does not suffer any stability problem. This simple mechanism can be 8 For another recent way to overcome this problem and to access the same parameter region, see [16].…”

Shift symmetry and Higgs inflation in supergravity with observable gravitational waves

“…We also analyze the impact of the one-loop radiative corrections (RCs) [51] on our results and find that these can be kept under control provided that the relevant renormalization scale is conveniently chosen [52]. We, finally, show that the ultraviolet (UV) cut-off scale [53][54][55][56][57] in these models coincides with the Planck scale and so concerns regarding their naturalness can be safely eluded.…”