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We derive lower bounds for the Higgs-curvature coupling from vacuum stabilityduring inflation in three inflationary models: quadratic and quartic chaoticinflation, and Starobinsky-like power-law inflation. In contrast to mostprevious studies we take the time-dependence of the Hubble rate into accountboth in the geometry of our past light-cone and in the Higgs effectivepotential, which is approximated with three-loop renormalisation groupimprovement supplemented with one-loop curvature corrections. We find that inall three models, the lower bound is $\xi\gtrsim 0.051\ldots 0.066$ dependingon the top quark mass. We also demonstrate that vacuum decay is most likely tohappen a few $e$-foldings before the end of inflation.

Vacuum decay constraints on the Higgs curvature coupling from inflation