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.
