Natural Higgs Inflation, Gauge Coupling Unification, and Neutrino Masses

We present a class of non-supersymmetric models in which so-called critical Higgs inflation ($\xi<100$) naturally can be realized without using specific values for Higgs and top quark masses. In these scenarios, the Standard Model (SM) vacuum stability problem, gauge coupling unification, neutrino mass generation and Higgs inflation mechanism are linked to each other. We adopt in our models Type I seesaw mechanism for neutrino masses. An appropriate choice of the Type I Seesaw scale allows us to have an arbitrarily small but positive value of SM Higgs quartic coupling around the inflation scale. We present a few benchmark points where we show that the scalar spectral indices are around 0.9626 and 0.9685 for the number of e-folding $N=50$ and $N=60$ respectively. The tensor-to-scalar ratios are order of $10^{-3}$. The running of the scalar spectral index is negative and is order of $10^{-4}$.