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

The Standard Model Higgs potential is known to be metastable, therefore Higgs Inflation requires an extension in order to stabilise the potential. Here we consider stabilisation by adding nQ ≤ 3 Vector-Like Quarks (VLQs) of mass mQ: T vector quarks transforming as ( 3, 1, 2/3) and B vector quarks transforming as ( 3, 1, -1/3). Requiring stability of the finite-temperature effective potential, and assuming mₜ equals its mean value, we find that the upper bounds on mQ for T quarks are 5.8 TeV (for nQ = 2) and 55 TeV (for nQ = 3). The corresponding absolute stability upper bounds are 4.4 TeV and 29 TeV. Small upper bounds are obtained for B quarks. For renormalisation in the Einstein frame (Prescription I) the predictions are almost indistinguishable from the classical values: nₛ = 0.966 and r = 3.3 × 10⁻³. Renormalisation in the Jordan frame (Prescription II) predicts larger values of nₛ and r, with nₛ generally in the range 0.980 to 0.990 and r of the order of 0.01. The predicted range of nₛ 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 constraint on mQ, with the T quark upper bound equal to 2.4 TeV for nQ = 2 and 13 TeV for nQ = 3. 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 nₛ that favour an early-time solution to the Hubble tension.