Critical point Higgs inflation in the Palatini formulation

A bstract 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 y t , we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling ξ . The spectral index n s can take any value in the observationally allowed range. The lower limit for the running is α s > − 3 . 5 × 10 − 3 , and α s 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.