  We study quantum effects in Higgs inflation in the Palatini formulation of
gravity, in which the metric and connection are treated as independent
variables. We exploit the fact that the cutoff, above which perturbation theory
breaks down, is higher than the scale of inflation. Unless new physics above
the cutoff leads to unnaturally large corrections, we can directly connect
low-energy physics and inflation. On the one hand, the lower bound on the top
Yukawa coupling due to collider experiments leads to an upper bound on the
non-minimal coupling of the Higgs field to gravity: $\xi \lesssim 10^8$. On the
other hand, the Higgs potential can only support successful inflation if $\xi
\gtrsim 10^6$. This leads to a fairly strict upper bound on the top Yukawa
coupling of $0.925$ (defined in the $\overline{\text{MS}}$-scheme at the energy
scale $173.2\,\text{GeV}$) and constrains the inflationary prediction for the
tensor-to-scalar ratio. Additionally, we compare our findings to metric Higgs
inflation.
