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The running of the Higgs self coupling may lead to numerous phenomena inearly universe cosmology. In this paper we introduce a scenario where the Higgsrunning induces turns in the trajectory passing a region with tachyonic mass,leading to a temporal tachyonic growth in the curvature power spectrum. Thiseffect induced by the Higgs leaves phenomena in the form of primordial blackholes and stochastic gravitational waves, where proposed GW observatories willbe able to probe in the near future.

The Inflaton that Could : Primordial Black Holes and Second Order Gravitational Waves from Tachyonic Instability induced in Higgs-$R^2$ Inflation