Higgs criticality from inflation

Skimming a paper on "the quantum critical Higgs", that eschews theorizing about the mechanism of this quantum criticality, I wonder... could inflation itself ever be a quantum phase transition ending at a critical point? This comes to mind because the observed Higgs boson mass doesn't just place the electroweak vacuum at the edge of stability, it is also close to a lower limit below which Higgs inflation isn't possible.