  We derive lower bounds for the Higgs-curvature coupling from vacuum stability
during inflation in three inflationary models: quadratic and quartic chaotic
inflation, and Starobinsky-like power-law inflation. In contrast to most
previous studies we take the time-dependence of the Hubble rate into account
both in the geometry of our past light-cone and in the Higgs effective
potential, which is approximated with three-loop renormalisation group
improvement supplemented with one-loop curvature corrections. We find that in
all three models, the lower bound is $\xi\gtrsim 0.051\ldots 0.066$ depending
on the top quark mass. We also demonstrate that vacuum decay is most likely to
happen a few $e$-foldings before the end of inflation.
