Did our Universe Tunnel out of the Wrong Higgs Vacuum?

TL;DR

The paper addresses whether the Universe began in the EW vacuum or the deeper Higgs vacuum and how inflation and reheating shape this history. It shows that inflation can either preferentially select EW regions if enough $e$-folds occur (with a lower bound around $n_{\text{e-folds}}\gtrsim 37$), or, starting from the wrong vacuum, reheating can dynamically drive a first-order phase transition back to the EW vacuum through rising thermal corrections. The transition features thick-walled bubbles, a small energy fraction $\alpha$, and ultra-relativistic wall speeds, producing predominantly sound-wave-driven gravitational waves with peak frequencies around $\sim 10$ GHz and amplitudes $\Omega_{\text{GW}} \lesssim 10^{-13}$, making detection challenging but offering a clean Standard Model benchmark and potential high-energy BSM implications via bubble dynamics. The work thus connects Higgs metastability, inflation, and reheating to a testable gravitational-wave signature and to possible Beyond-Standard-Model phenomena, motivating future ultra-high-frequency GW experiments and continued theoretical exploration of early-Universe Higgs dynamics.

Abstract

This paper explores various aspects and implications of the initial configuration of the Standard Model (SM) Higgs field at the beginning of our Universe. It is well known that the SM Higgs field features a deeper, more stable minimum at large field values. While it is possible that our Universe began and remained in the electroweak vacuum at all times, this scenario is extremely fine-tuned from the point of view of initial conditions. This fine-tuning can be ameliorated by the exponential expansion of spacetime during inflation: intriguingly, this requires at least $\sim 40$ e-folds of inflation, tantalizingly close to the $50-60$ e-folds expected from horizon and flatness considerations. The Higgs could thus provide the reason for a prolonged epoch of inflation in our cosmic history. Otherwise, the most natural initial state corresponds to our Universe initialized in the more stable but "wrong" Higgs vacuum, and subsequently driven dynamically to the weak scale vacuum during reheating. An important, hitherto unexplored aspect of this dynamics is that the barrier between the two vacua persists when the electroweak vacuum becomes energetically favorable, becoming arbitrarily small as the temperature increases, and therefore triggers a first-order phase transition. This transition produces ultra-high (megahertz to gigahertz) frequency gravitational waves (GWs), serving as a challenging but unique SM target for GW experiments. Novel pathways for various beyond the Standard Model phenomena such as the production of dark matter and baryon asymmetry also become possible in this configuration.

Figures (5)

• Figure 1: Thermally corrected Higgs potential for increasing temperatures: zero temperature (blue); critical temperature $T_c$ where the two vacua become degenerate (orange); nucleation temperature $T_*$ where the phase transition becomes efficient (green), crossover temperature $T_{co}$ where the higher minimum disappears (red), and maximum temperature $T_m$ reached by the radiation bath (purple).
• Figure 2: The bounce action $S_3/T$ as a function of temperature. As $T\to T_{co}$, the potential barrier separating the two vacua becomes vanishingly small, quickly driving the action to $\mathcal{O}(1)$ values, inevitably leading to rapid tunneling.
• Figure 3: Temperature of radiation bath as a function of time for various choices of inflaton decay rate.
• Figure 4: Higgs field profile in a critical bubble.
• Figure 5: Various possibilities for the initial configuration of the Higgs field ($h_i$) at the beginning of the Universe and its interplay with the scale of inflation $H$, for $\Lambda_I=10^{11}$ GeV and $\Lambda_{UV}=10^{14}$ GeV.