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We study the gauge-independent observables associated with two interestingstationary configurations of the Standard Model Higgs potential (extrapolatedto high energy according to the present state of the art, namely the NNLO): i)the value of the top mass ensuring stability of the SM electroweak minimum, andii) the value of the Higgs potential at a rising inflection point. We examinein detail and reappraise the experimental and theoretical uncertainties whichplague their determination, finding that: i) stability of the SM is compatiblewith the present data at the 1.5 sigma level; ii) despite the large theoreticalerror plaguing the value of the Higgs potential at a rising inflection point,application of such configuration to models of primordial inflation displays a3 sigma tension with the recent bounds on the tensor-to-scalar ratio ofcosmological perturbations.

Stationary configurations of the Standard Model Higgs potential: electroweak stability and rising inflection point