A Cosmological Signature of the SM Higgs Instability: Gravitational Waves (1804.07732v3)

Abstract: A fundamental property of the Standard Model is that the Higgs potential becomes unstable at large values of the Higgs field. For the current central values of the Higgs and top masses, the instability scale is about $10^{11}$ GeV and therefore not accessible by colliders. We show that a possible signature of the Standard Model Higgs instability is the production of gravitational waves sourced by Higgs fluctuations generated during inflation. We fully characterise the two-point correlator of such gravitational waves by computing its amplitude, the frequency at peak, the spectral index, as well as their three-point correlators for various polarisations. We show that, depending on the Higgs and top masses, either LISA or the Einstein Telescope and Advanced-Ligo, could detect such stochastic background of gravitational waves. In this sense, collider and gravitational wave physics can provide fundamental and complementary informations. Furthermore, the consistency relation among the three- and the two-point correlators could provide an efficient tool to ascribe the detected gravitational waves to the Standard Model itself. Since the mechanism described in this paper might also be responsible for the generation of dark matter under the form of primordial black holes, this latter hypothesis may find its confirmation through the detection of gravitational waves.

• The paper demonstrates that SM Higgs field fluctuations during inflation can generate distinct gravitational waves with computed amplitudes and spectral indices.
• The analysis predicts observable GW signals with energy density around 10⁻⁸ and a transition from blue to red spectral tilt, suggesting detectability by LISA and similar detectors.
• The study bridges particle physics and cosmology, hinting at dark matter implications through potential primordial black hole formation.

Analyzing the Higgs Instability and Gravitational Wave Generation

The paper at hand investigates a potential cosmological signature of the Standard Model (SM) Higgs boson instability manifesting as gravitational waves (GWs). This research provides a detailed examination of how fluctuations in the Higgs field during inflationary cosmology could lead to observable gravitational wave signatures—a topic that holds great significance in theoretical particle physics and cosmology.

Overview

The Standard Model of particle physics postulates that the Higgs potential becomes unstable when the Higgs field reaches high energies, approximately around $10^{11}$ GeV. While currently inaccessible through direct collider experiments, the authors propose that this Higgs field instability could produce detectable signals in the form of gravitational waves. These GWs are generated as secondary sources due to the Higgs field fluctuations during inflation.

Detailed Findings

1. Higgs Instability and Gravitational Waves:
   • The authors describe a scenario where Higgs fluctuations, induced during the inflationary phase, can source gravitational waves.
   • They extensively model the GW spectrum, computing characteristics such as amplitude, frequency at the peak, and the spectral index.
2. Detection Possibilities:
   • The paper posits that, depending on the exact masses of the Higgs and top quark, upcoming and planned gravitational wave detectors like LISA, the Einstein Telescope, and Advanced-LIGO could potentially observe this stochastic GW background.
   • This synchronization of collider physics with GW detection could provide complementary insights into the Higgs sector.
3. Spectral Characteristics:
   • The paper forecasts that the power spectrum of these gravitational waves would have a typical energy density $\Omega_{\rm GW} \sim 10^{-8}$ at the peak frequency.
   • Interestingly, the spectral index is predicted to vary, showing a "blue" tilt (increasing amplitude with frequency) with $n_T \simeq 3$ for frequencies below the peak, transitioning to a "red" tilt (decreasing amplitude) of $n_T \simeq -0.6$ above the peak.
4. Implications for Dark Matter and Cosmology:
   • An additional implication raised is the potential connection to dark matter, suggesting these Higgs fluctuations may have produced primordial black holes, a proposed constituent of dark matter.
   • This connection between fundamental particle physics and cosmological phenomena offers a promising direction for resolving some outstanding theoretical and empirical puzzles.

Implications and Future Directions

The findings of this research carry several theoretical implications:

• High-Energy Physics Risk: The described mechanisms open a novel observational horizon, enabling indirect investigation of super-high energy physics domains that can otherwise only be hypothesized.
• Inflationary Cosmology Insights: Understanding the explicit dynamics of the Higgs field during inflation could provide crucial insights into early Universe models and the behavior of fundamental forces at unprecedented energies.
• Dark Matter Exploration: Should primordial black holes be detected, perhaps unusual in mass distributions predicted by other models, researchers could lean on this framework to explore their potential SM origin.

Given these implications, the paper bridges gaps between particle physics and cosmology, making it an essential reference for future explorations aiming to deepen our understanding of the Universe’s birth and its fundamental laws. It emphasizes the need for further experimental advancements in both particle collider and gravitational wave research to confirm or refute these propositions. Such interdisciplinary studies are likely to play pivotal roles in the evolution of theoretical physics and cosmology in the forthcoming years.