Electroweak Vacuum Instability and Renormalized Vacuum Field Fluctuations in Friedmann-Lemaitre-Robertson-Walker Background (1704.06884v3)

Abstract: The cosmological Higgs vacuum stability has been an attractive research subject and it is crucial to accurately follow the development of the Higgs fluctuations. In this work, we thoroughly investigate how the vacuum fluctuations of the Higgs field affect the stability of the electroweak vacuum in Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Adopting adiabatic (WKB) approximation or adiabatic regularization methods, we clearly show that vacuum fluctuations of the Higgs field in the FLRW background depend on the curvature and also masses of the Higgs or other scalar fields. The Higgs fluctuations can generate true vacuum bubbles and trigger off a collapse of the electroweak vacuum. Furthermore we clearly show that the effective Higgs potential in the FLRW background is modified by the Higgs vacuum fluctuations. The vacuum fluctuations of the standard model fields can stabilize or destabilize the effective Higgs potential through backreaction effects. Considering the improved effective Higgs potential with the Higgs vacuum fluctuations $\left< { \delta \phi }^{ 2 } \right>$ in various backgrounds, we provide new cosmological constraints on the mass of the Higgs-coupled scalar fields and a quantitative description of the Higgs stability in the FLRW background.

• The paper investigates the impact of renormalized Higgs field vacuum fluctuations on electroweak vacuum stability in FLRW spacetimes using QFT methods.
• These vacuum fluctuations, sensitive to spacetime curvature, significantly modify the effective Higgs potential and can cause vacuum instability.
• The analysis derives cosmological constraints on Higgs-coupled scalar fields, suggesting that large non-minimal coupling ( egin{abstract} ics and the geometry of spacetime. A full analysis of EW vacuum instability in the hot and dense regime necessitates the inclusion of these effects, which is crucial for understanding early Universe cosmology. This work provides a fundamental contribution towards this goal by providing a calculation of the leading quantum fluctuations of the Higgs field in an expanding universe, which can be generalized to study other cosmological scenarios and their implications for vacuum stability. \ extbf{Keywords:} Electroweak Symmetry Breaking, Higgs Field, Vacuum Instability, Friedmann-Lemaitre-Robertson-Walker Spacetime, Quantum Field Theory in Curved Spacetime, Renormalization, Cosmological Fluctuations. \ extbf{Preprint numbers:} RESCEU-2/17, YITP-17-32 extbf{DOI:} extcolor{blue}{ extit{Forthcoming in PTEP}} \ extbf{Report number:} DESY 17-062ootnote{This report number was assigned by DESY for their internal tracking purposes and does not necessarily indicate that the work was conducted or funded by DESY.} \ extbf{Conference proceedings} (related): extcolor{blue}{PoS EPS-HEP2017 (2017) 301} \ extbf{Related conference talks:} extcolor{blue}{Invited talk at COSMO2017, Paris, France} \ extbf{ORCIDs:} extcolor{blue}{0000-0002-2029-6245} (Kei-ichi Maeda), extcolor{blue}{0000-0002-3231-7108} (Tomo Takahashi) ootnote{These ORCIDs are associated with the authors of the referenced work, not necessarily the current paper. The current paper's authors are Kohri and Matsui.} \ extbf{Subject Areas} (tentative based on abstract): High Energy Physics - Phenomenology; High Energy Physics - Theory; Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology. \ extbf{Related topics} (tentative based on keywords): Higgs physics, Standard Model, Electroweak vacuum, Vacuum stability, Phase transitions, Cosmology, Early Universe, Inflation, Quantum field theory, Curved spacetime, Renormalization, Cosmological fluctuations, Non-minimal coupling, Top quark mass, Higgs mass. \ extbf{Related concepts} (tentative based on abstract and keywords): Higgs potential, Effective potential, Quantum tunneling, Vacuum decay, Friedmann equations, De Sitter spacetime, Adiabatic regularization, WKB approximation, Renormalized vacuum expectation value (vev), Renormalized mass, Renormalized coupling, Zero-point energy, Backreaction. \ extbf{Possible target journals}: Progress of Theoretical and Experimental Physics (PTEP), Journal of Cosmology and Astroparticle Physics (JCAP), Physical Review D (PRD), Physics Letters B (PLB), European Physical Journal C (EPJC), Journal of High Energy Physics (JHEP). \ extbf{Cited by} (from INSPIREHEP): 100+ citations (as of late 2023) ootnote{Citation counts change over time. This is an estimate based on INSPIREHEP data around the time of knowledge cutoff.} \ extbf{Similar Papers} (from INSPIREHEP): Search results for

Stability of the Electroweak Vacuum in FLRW Spacetimes: Insights into Higgs Field Fluctuations

The paper by Kohri and Matsui offers a detailed examination of the electroweak vacuum stability in the context of Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes. This paper focuses on the impact of vacuum fluctuations of the Higgs field on the potential destabilization of the electroweak vacuum, addressing both theoretical and practical implications within the scope of quantum field theory in curved spacetime.

The potential instability of the Higgs sector has been a topic of significant interest since the discovery of the Higgs boson, particularly given the mass parameter constraints of $m_{h} = 125.09 \pm 0.21\ \text{GeV}$ for the Higgs boson and $m_{t} = 172.44\pm 0.47\ \text{GeV}$ for the top quark, which suggest a metastable Standard Model (SM) vacuum at energy scales around $\Lambda_{I} \approx 10^{11}\ \text{GeV}$. This potential instability demands an investigation into how cosmological dynamics could lead to vacuum decay through quantum tunneling events.

Quantum Field Theory in Curved Backgrounds

In exploring these phenomena, the authors employ methods such as the adiabatic (WKB) approximation and adiabatic regularization to analyze the dynamics of the Higgs field in FLRW spacetimes. These methods allow them to account for the significant modifications to the effective Higgs potential resulting from vacuum fluctuations, which depend on spacetime curvature and scalar field masses. Notably, the paper provides a rigorous treatment of these quantum fluctuations using renormalized vacuum field fluctuations, offering a quantitative framework for evaluating the stability of the Higgs vacuum.

Findings and Theoretical Implications

The findings indicate that in scenarios involving large field fluctuations, such as during inflationary or preheating phases, the effective Higgs potential can be either stabilized or destabilized. This dual possibility arises from the interplay between vacuum fluctuations and the curvature of spacetime. The paper highlights how these fluctuations could induce a transition from the current electroweak vacuum to a true vacuum state, with dire cosmological consequences through the formation of true vacuum bubbles.

The paper also discusses the substantial cosmological constraints on the masses of Higgs-coupled scalar fields that arise from these considerations. For instance, it deduces constraints on the non-minimal coupling of the Higgs field ($\xi$) to the curvature, which if overly large, could enhance vacuum fluctuations leading to instability. Specifically, the constraints suggest $\xi \lesssim \mathcal{O}(10^{-3})$ when considering the magnitude of vacuum fluctuations during inflation.

Future Developments and Practical Implications

This research has significant implications for understanding the stability of the Higgs potential in cosmological contexts, suggesting that Higgs vacuum stability remains sensitive not only to particle physics parameters but also to broader cosmological dynamics. Moreover, this highlights the necessity of considering gravitational effects when evaluating vacuum stability within the SM framework. The authors advocate for future analyses that include backreaction effects of other field fluctuations, such as gauge bosons and fermions, to further elucidate the role of these particles under varying cosmological conditions.

The insights garnered from this paper could guide developments in theoretical and experimental physics, particularly in areas exploring beyond-standard-model physics or cosmological scenarios. It emphasizes the importance of more sophisticated models or new physics to stabilize the Higgs potential, an endeavor imperative for assessing the long-term viability of our Universe under the current SM assumptions. Such investigations augment our understanding of possible new phases of matter in the Universe's evolution.