Critical point Higgs inflation in the Palatini formulation

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 $\lambda$ and the top Yukawa coupling $y_t$, we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling $\xi$. The spectral index $n_s$ can take any value in the observationally allowed range. The lower limit for the running is $\alpha_s>-3.5\times10^{-3}$, and $\alpha_s$ can be as large as the observational upper limit. Running of the running is small. The tensor-to-scalar ratio is $2.2\times 10^{-17}<r<2\times10^{-5}$. 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.