On electroweak metastability and Higgs inflation

For the central values of the relevant experimental inputs, that is the strong coupling constant and the top quark and Higgs masses, the effective Higgs potential displays two minima, one at the electroweak scale and a deeper one at high energies. We review the phenomenology of the Higgs inflation model, extending the Standard Model to include a non-minimal coupling to gravity; as recently shown [1], even configurations that would be metastable in the Standard Model, become viable for inflation if the non-minimal coupling is large enough to flatten the Higgs potential at field values below the barrier between the minima.

💡 Research Summary

The paper reviews the interplay between electroweak vacuum metastability in the Standard Model (SM) and the possibility of Higgs‑driven cosmic inflation once a non‑minimal coupling to gravity is introduced. Using the latest central values of the strong coupling αₛ(5), the top‑quark pole mass m_t and the Higgs mass m_H, the authors confirm that the SM effective Higgs potential V_eff(φ) develops two minima: the familiar electroweak one and a deeper minimum at field values close to the Planck scale. Renormalization‑group evolution at three‑loop accuracy shows that for the central inputs the electroweak vacuum is metastable; the critical top‑mass at which the two minima become degenerate is m_ct ≈ 171.0588 GeV. Small deviations δ_t = m_t/m_ct – 1 of order 10⁻⁵–10⁻⁶ produce characteristic shapes such as an inflection point or a shallow secondary vacuum.

A pure SM Higgs cannot sustain slow‑roll inflation because the potential is either too steep or the required flat region lies beyond the barrier separating the minima. The authors therefore consider the Higgs‑inflation model of Bezrukov and Shaposhnikov, adding a term ξ|H|²R to the Lagrangian. In the metric formulation this non‑minimal coupling flattens the potential for field values φ ≳ M_P/√ξ, where M_P is the reduced Planck mass. For ξ ≈ 500–800 the flattened region satisfies the slow‑roll parameters ε, η ≪ 1, yielding N ≈ 60 e‑folds, a scalar spectral index n_s ≈ 0.967 and a tensor‑to‑scalar ratio r ≈ 0.003, both comfortably within the latest Planck constraints (Δ_R² ≈ 2.1×10⁻⁹, r < 0.036). The corresponding inflationary energy scale is V^{1/4}_i ≈ 7.6×10¹⁵ GeV.

Crucially, the flattening effect allows configurations that would be metastable in the SM to become viable inflaton candidates. The paper shows, via Figures 2 and 3, how the same SM parameters that produce an inflection‑point potential can be rescued by a modest ξ ≈ 800, leading to a smooth plateau and successful inflationary predictions. Moreover, the required ξ decreases as the top mass increases; for top masses close to the metastability boundary ξ can be as low as ~500, which alleviates concerns about unitarity violation (the associated cutoff Λ ≈ M_P/ξ lies above 10¹⁶ GeV).

The authors discuss the theoretical subtleties, including the choice between metric and Palatini formulations and the unitarity issue, noting that with ξ in the few‑hundred range the effective field‑theory description remains reliable. They emphasize that a more precise determination of the top‑quark mass would dramatically sharpen the predictions, potentially confirming or ruling out Higgs‑inflation scenarios that rely on metastable vacua.

In summary, the work demonstrates that electroweak metastability does not preclude Higgs‑driven inflation; a sufficiently large non‑minimal gravitational coupling can flatten the potential below the barrier, yielding inflationary observables compatible with current cosmological data while keeping theoretical consistency under control. This extends the viable parameter space of Higgs inflation and highlights the importance of future precision measurements of m_t and αₛ.