Higgs-Induced Gravitational Waves: the Interplay of Non-Minimal Couplings, Kination and Top Quark Mass

TL;DR

The paper addresses how a non-minimally coupled SM Higgs, acting as a spectator after inflation during a stiff, kination-like epoch, can heat the Universe and generate a stochastic gravitational-wave background (SGWB) whose properties encode the high-scale Higgs potential. Using a combination of RG-improved Higgs running and semi-analytic lattice-based parametric formulas, it links the SGWB features to the inflationary scale, the non-minimal coupling, and the top-quark mass, and distinguishes absolute stability, instability, and new-physics scenarios. The main finding is that HIPTs produce a peaked GW spectrum with a strong inflationary tail that can reveal the Higgs potential at ultra-high energies and offer a minimal reheating mechanism, independent of SM vacuum tunnelling. The results imply that gravitational-wave observations could constrain the top-quark mass and high-scale Higgs dynamics, potentially signaling BSM physics through spectrum shape and peak placement.

Abstract

We explore a minimal scenario where the sole Standard-Model Higgs is responsible for reheating the Universe after inflation, produces a significant background of gravitational waves and maintains the full classical stability of the electroweak vacuum. As the Higgs self-coupling runs toward negative values at high energy scales, a non-minimal interaction with curvature during a stiff background expansion era drives the Higgs fluctuations closer to the instability scale. This curvature-induced tachyonic instability leads to an intense production of Higgs particles, accompanied by a stochastic gravitational-wave background. The characteristic features of such signal can be directly correlated to the inflationary scale, the non-minimal coupling parameter and the top quark Yukawa coupling. We distinguish between three possible scenarios: absolute stability with low top quark masses, potential vacuum instability, and absolute stability with new physics above the instability scale. Our findings suggest that the detection of a peaked background of gravitational waves together with its inflationary tail has the potential to unveil the features of the Higgs effective potential at very high energy scales while providing a minimal explanation for the reheating phase and the emergence of the Standard-Model plasma in the early Universe. Unlike other studies in the literature, the generation of gravitational waves in our scenario does not depend on the quantum instability of the Standard Model vacuum.

Figures (9)

• Figure 1: Higgs effective potential with a non-minimal gravitational coupling at the onset of kination for three prototypical scenarios: absolute stability (green line, $m_t=170.8 \textrm{ GeV}$), instability (red line, $m_t=171.3 \textrm{ GeV}$), stability with new physics as sextic operators at a typical scale ${\Lambda=10^{15} \textrm{ GeV}}$ (blue line, $m_t=171.3 \textrm{ GeV}$). The cut-off of the effective gravitational theory is given by $\Lambda_{\xi}=9.2\times10^{15} \textrm{ GeV}$. The cosmological parameters have been set to $\nu=20$ and $\mathcal{H}_{\rm kin}=10^{9} \textrm{ GeV}$.
• Figure 2: Energy density $h^2\Omega_{\rm GW,0}$ and peak frequency $f_{\rm GW,0}$ of the GW spectrum at the present day as a function of $\mathcal{H}_{\rm kin}$ and $\nu$. The top-quark mass has been set to be compatible with the absolute stability of the electroweak vacuum $m_t=170.8 \textrm{ GeV}$. The coloured regions indicate the areas excluded by the proximity to the effective-theory cut-off scale (light blue), by the bound on the inflationary scale from CMB measurements (green), by the number of effective degrees of freedom at BBN (grey), and by the minimum (re)heating temperature (blue).
• Figure 3: SGWB signal from a Higgs HIPT for different breaking scales compared to sensitivity curves of proposed GW detectors: Laser Interferometer Space Antenna (LISA) amaroseoane2017laserinterferometerspaceantennaRobson:2018ifk, Big Bang Observer (BBO) Crowder:2005nrCorbin:2005ny, UltimateDECIGO Seto:2001qfYagi:2011wgKawamura:2020pcg, Einstein Telescope (ET) Punturo:2010zzBranchesi:2023mws, and Cosmic Explorer (CE) LIGOScientific:2016wofReitze:2019iox. The non-minimal coupling parameter is set to $\nu=20$ while the top-quark mass $m_t=170.8 \textrm{ GeV}$ ensures the absolute stability of the Higgs vacuum.
• Figure 4: Energy density $h^2\Omega_{\rm GW,0}$ and peak frequency $f_{\rm GW,0}$ of the GW spectrum at the present day for different values of the top-quark mass and the non-minimal coupling parameter, with a fixed phase-transition scale $\mathcal{H}_{\rm kin}=10^{12} \text{ GeV}$. Red regions are forbidden because classically unstable, while light-blue shaded areas do not satisfy the 1% upper bound on the gravitational theory cut-off scale $\langle h^2 \rangle < 10^{-2} M_P^2 / \xi^2$.
• Figure 5: GW signal from the non-minimally coupled Higgs for different heating efficiencies of an enhanced heating sector $\Theta_{\text{ht}}^{\chi}$ compared to sensitivity curves of proposed GW detectors. The model parameters have been set to $\nu=20$ and $m_t=170.8 \textrm{ GeV}$ for a kination scale of $\mathcal{H}_{\rm kin}=10^{12} \textrm{ GeV}$.