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

We study the gauge-independent observables associated with two interesting stationary configurations of the Standard Model Higgs potential (extrapolated to high energy according to the present state of the art, namely the next-to-next-to-leading order): i) the value of the top mass ensuring the stability of the SM electroweak minimum and ii) the value of the Higgs potential at a rising inflection point. We examine in detail and reappraise the experimental and theoretical uncertainties which plague their determination, finding that i) the stability of the SM is compatible with the present data at the 1.5 sigma level and ii) despite the large theoretical error plaguing the value of the Higgs potential at a rising inflection point, the application of such a configuration to models of primordial inflation displays a 3 sigma tension with the recent bounds on the tensor-to-scalar ratio of cosmological perturbations.