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The measured Standard Model parameters lie in a range such that the Higgspotential, once extrapolated up to high scales, develops a minimum of negativeenergy density. This has important cosmological implications. In particular,during inflation, quantum fluctuations could have pushed the Higgs field beyondits potential barrier, triggering the formation of anti-de Sitter regions, withfatal consequences for our universe. By requiring that this did not happen, onecan in principle connect (and constrain) Standard Model parameters with theenergy scale of inflation. In this context, we highlight the sensitivity of thefate of our vacuum to seemingly irrelevant physics. In particular, thedeparture of inflation from an exact de Sitter phase, as well asPlanck-suppressed derivative operators, can, already and surprisingly, play adecisive role in (de)stabilizing the Higgs during inflation. Furthermore, inthe stochastic dynamics, we quantify the impact of the amplitude of the noisediffering from the one of a massless field, as well as of going beyond theslow-roll approximation by using a phase-space approach. On a general ground,our analysis shows that relating the period of inflation to precision particlephysics requires a knowledge of these "irrelevant" effects.

Higgs vacuum (in)stability during inflation: the dangerous relevance of de Sitter departure and Planck-suppressed operators