Critical point Higgs inflation in the Palatini formulation

Abstract

We study Higgs inflation in the Palatini formulation with the renormalisation group improved potential in the case when loop corrections generate a feature similar to an inflection point. Assuming that there is a threshold correction for the Higgs quartic coupling λ and the top Yukawa coupling yt, we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling ξ.The spectral index ns can take any value in the observationally allowed range. The lower limit for the running is αs> −3.5 × 10−3, and αs can be as large as the observational upper limit. Running of the running is small. The tensor-to-scalar ratio is 2.2×10−17< r < 2 × 10−5. We find that slow-roll can be violated near the feature, and a possible period of ultra-slow-roll contributes to the widening of the range of CMB predictions. Nevertheless, for the simplest tree-level action, the Palatini formulation remains distinguishable from the metric formulation even when quantum corrections are taken into account, because of the small tensor-to-scalar ratio.

Reheating in Models with Non-minimal Coupling in metric and Palatini formalisms

“…These constraints will be more stringent for future observations such as CMB-S4 [40] and LiteBIRD [41], lying beyond the 2σ expected bounds. This fact also can be used to distinguish metric Higgs inflation models from Palatini cases [48,[67][68][69][70][71][72]. Note that the early stage of the reheating (namely 'preheating') of Palatini Higgs inflation possesses w −1 [73], which makes the compatibility to the observations worse if the reheating processes has an averaged equation of state w reh < 1/3.…”

Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation

“…Smaller quartic coupling λ at the inflationary scale due to running would imply smaller ξ, ameliorating the problem. It is also possible to get a smaller ξ by changing the inflationary dynamics by tuning the running of the Higgs quartic coupling λ to create a critical point, hilltop or another feature at the inflationary scale [35,41,42,46,[57][58][59][60][61][62][63][64][65][66]69]. In the Palatini case, the action can also be changed by including new non-metricity or torsion terms [122,125,128].…”

“…As discussed in [69], none of the above scales is directly related to scattering processes, which indeed play no role during inflation. The variance of the field is H/(2π), which is below (although close to) the cutoff, but it is not clear why this or the other scales should be directly compared to scattering energy.…”

“…In particular, the inflationary predictions are different in the Palatini formulation [61, 65-67, 69, 82, 103, 119-125, 125-128], and in the teleparallel formulation [124]. In the Palatini case, unitarity is expected to be violated at energies ∼ M Pl / √ ξ, parametrically higher than in the metric formulation, although in the Palatini case the value of ξ is also typically larger [67,69,82,103,120,126]. The tree-level 2 → 2 scattering amplitudes for the Higgs doublet and the resulting unitarity bound have been calculated in the metric formulation in [78,79], and one scattering amplitude was calculated in both the metric and the Palatini formulation in [103].…”

On UV-completion of Palatini-Higgs inflation

“…There exists a possibility that the self-coupling of the Higgs field λ is tuned to be small at inflationary energy scales, which is known as the critical Higgs scenario[31][32][33][34].…”