Higgs Inflation via the Metastable Standard Model Potential, Generalised Renormalisation Frame Prescriptions and Predictions for Primordial Gravitational Waves

Abstract

Higgs Inflation via a metastable Standard Model Higgs Potential is possible if the effective Planck mass in the Jordan frame increases after inflation ends. Here we consider the predictions of this model independently of the dynamics responsible for the Planck mass transition. The classical predictions are the same as for conventional Higgs Inflation. The quantum corrections are dependent upon the conformal frame in which the effective potential is calculated. We generalise beyond the usual Prescription I and II renormalisation frame choices to include intermediate frames characterised by a parameter $\alpha$. We find that the model predicts a well-defined correlation between the values of the scalar spectral index $n_{s}$ and tensor-to-scalar ratio $r$. For values of $n_{s}$ varying between the 2-$\sigma$ Planck observational limits, we find that $r$ varies between 0.002 and 0.005 as $n_{s}$ increases, compared to the classical prediction of 0.003. Therefore significantly larger or smaller values of $r$ are possible, which are correlated with larger or smaller values of $n_{s}$. In addition, the model can be compatible with the larger values of $n_{s}$ predicted by Early Dark Energy solutions to the Hubble tension, with correspondingly larger values of $r$. The model can be tested via the detection of primordial gravitational waves by the next generation of CMB polarisation experiments.