Vector-like Quark Stabilised Higgs Inflation: Implications for Particle Phenomenology, Primordial Gravitational Waves and the Hubble Tension

The Standard Model (SM) Higgs potential is likely to be metastable, in which case Higgs Inflation requires an extension of the SM to sufficiently stabilise the Higgs potential. Here we consider stabilisation by adding $n_{Q} \leq 3$ Vector-Like Quarks (VLQs) of mass $m_{Q}$. We consider isosinglet $T$ and $B$ vector quarks. Requiring stability of the finite temperature effective potential, we find that the upper bounds on $m_{Q}$ for $T$ quarks are 5.8 TeV (for $n_{Q} = 2$) and 55 TeV (for $n_{Q} = 3$). The upper bounds are generally smaller for $B$ vector quarks and are sensitive to the $t$-quark mass. The inflation predictions depend upon the conformal frame in which the model is renormalised. For renormalisation in the Einstein frame (Prescription I) the predictions are almost indistinguishable from the classical values: $n_s = 0.966$ and $r = 3.3 \times 10^{-3}$. Renormalisation in the Jordan frame (Prescription II) predicts larger values of $n_{s}$ and $r$, with $n_{s}$ generally in the range 0.980 to 0.990 and $r$ of the order of 0.01. The predicted range of $n_{s}$ is consistent with the CMB range obtained in Hubble tension solutions which modify the sound horizon at decoupling, whilst the predicted values of $r$ will be easily observable by forthcoming CMB experiments. The observational upper bound on $r$ generally imposes a stronger upper bound on $m_{Q}$ in Prescription II than the requirement of stability. We conclude that VLQ-stabilised Higgs Inflation with Prescription II renormalisation favours 1-10 TeV vector-like quarks that will be accessible to future colliders, and predicts a tensor-to-scalar ratio that will be observable in forthcoming CMB experiments and values of $n_{s}$ that favour an early-time solution to the Hubble tension.