Calculate the stochastic gravitational-wave background predicted by the Higgs inflation EFT models

Compute the stochastic gravitational-wave background generated by the effective Higgs inflation models defined by the action S with non-minimal coupling U(h) and potential V(h) specified in Eq. (UV), which include higher-dimension operator corrections and a quasi–ultra slow-roll phase (implemented via the deformation v2 → v2 (1 + ε)). Determine the resulting spectrum (e.g., amplitude and frequency dependence) so that these models can be confronted with observations by experiments such as NanoGRAV and future gravitational-wave observatories.

Background

The paper develops a minimal effective field theory extension of Higgs inflation by introducing higher-dimension operators in both the non-minimal coupling U(h) and the potential V(h), enabling a slow-roll phase followed by a (quasi-)ultra slow-roll phase that amplifies curvature perturbations to produce primordial black holes.

The authors note that while these higher-dimension operators are suppressed at low energies, they could significantly affect the stochastic gravitational-wave background. They explicitly state that calculating this background is important and leave it for future work, highlighting a concrete, testable prediction of their models that remains uncomputed.