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

McDonald, John (2025) Vector-like Quark Stabilised Higgs Inflation: Implications for Particle Phenomenology, Primordial Gravitational Waves and the Hubble Tension. Journal of Cosmology and Astroparticle Physics, 2025 (3): 055. ISSN 1475-7516

Abstract

The Standard Model (SM) Higgs potential is very likely to be metastable, in which case Higgs Inflation is likely to require 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 $T$ vector quarks transforming under the SM gauge group as $({\bf 3}, {\bf 1}, 2/3)$ and $B$ vector quarks transforming as $({\bf 3}, {\bf 1}, -1/3)$. Requiring stability of the finite-temperature effective potential after instant reheating, and assuming that the $t$-quark mass $m_{t}$ equals the mean value of its experimental range, 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 corresponding absolute stability upper bounds are 4.4 TeV and 29 TeV. For $n_{Q} = 1$ there is stability only for $m_{t}$ at its -2-$\sigma$ value, in which case $m_{Q} \leq 1.6 \TeV$ for one $T$ quark. The upper bounds are generally smaller for $B$ vector quarks, with finite temperature stability for $m_{Q}$ less than 2.8 TeV (for $n_{Q} = 2$), 18 TeV (for $n_{Q} = 3$) and 1.0 TeV (for $n_{Q} = 1$). The upper bounds on $m_{Q}$ are sensitive to the $t$-quark mass, becoming smaller as $m_{t}$ increases. 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 $r = 3.3 \times 10^{-3}$. In this case the stability upper bounds on $m_{Q}$ apply. 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 constraint on $m_{Q}$ in Prescription II than the requirement of stability, with the $T$ quark upper bound equal to 2.4 TeV for $n_{Q} = 2$ and 13 TeV for $n_{Q} = 3$, assuming $m_{t}$ equals its mean value. $n_{Q} = 1$ is generally ruled out by the large value of $r$. The $m_{Q}$ upper bounds rapidly decrease with decreasing $r$. 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.