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.
Highlights
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
The SM and chiral SM RG equations augmented with threshold jumps at the unitarity breaking scale have been applied to Higgs inflation in the hilltop case [48] in both the metric and the Palatini formulation, and to features similar to an inflection point in the metric formulation [41]. (See [50] for the New Higgs inflation case.) We extend these studies to the case when the RG running creates an inflection point or a similar feature, often generically called a critical point, in the Palatini formulation
We have studied the range of predictions for Palatini Higgs inflation in the case when loop corrections generate a critical point in the potential, a feature similar to an inflection point
Summary
The Lagrangian of the SM coupled non-minimally to the Ricci scalar is (not writing explicitly the non-radial part of the Higgs, which enters only via its effect on RG running). Where gαβ is the metric, Rαβ is the Ricci tensor, M is a mass scale, h is the radial Higgs field, ξ is the non-minimal coupling,. The Ricci tensor is built from the connection Γγαβ, and as we consider the Palatini formulation, it is independent of the metric. We make a conformal transformation to the Einstein frame and define the new scalar field χ with minimal coupling to gravity and canonical kinetic term [1, 51]: gαβ → (1 + ξh2)−1gαβ , dχ. Where we have taken into account that in the inflationary region h v. Which is small on the inflationary plateau
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