[Paper Review] When Higgs Meets Starobinsky in the Early Universe

Mahdi Torabian|arXiv (Cornell University)|Oct 7, 2014

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes that non-minimal coupling of the Higgs field to a higher-curvature gravity theory—specifically Starobinsky-type inflation—can stabilize the electroweak vacuum without fine-tuning, resolving metastability issues in the Standard Model. The mechanism enhances the physical Higgs self-coupling, making it observable at future colliders, with predictions that deviate from the Standard Model by up to ∼10% for |ξ| ≲ 10¹⁰.

ABSTRACT

The measurement of the Higgs mass at the LHC has confirmed that the Standard Model electroweak vacuum is a shallow local minimum and is not absolutely stable. In addition to a probable unacceptably fast tunneling to the deep true minimum, it is not clear how the observable present-day vacuum could be reached from the early Universe particularly following inflation. In this note it is shown that these problems can be alleviated if the Higgs field is non-minimally coupled to a higher-curvature theory of gravity which is effective in deriving inflation a la Starobinsky. Moreover, it implies that the Higgs self-coupling could be enhanced and have an observable effect at the next generation of particle colliders.

Motivation & Objective

• To resolve the metastability of the electroweak vacuum in the Standard Model, which is a shallow local minimum with a tiny barrier to a deeper true vacuum.
• To address the fine-tuning problem in reheating the electroweak vacuum after inflation, where the Higgs field must be precisely initialized near the false vacuum.
• To explore whether quantum gravity effects via higher-curvature gravity can naturally stabilize the Higgs potential without introducing new particles or interactions.
• To predict observable deviations in the Higgs self-coupling due to mixing with a heavy scalar state arising from the non-minimal coupling.
• To constrain the non-minimal coupling parameter ξ using LHC data and perturbativity bounds, linking early-universe inflation to electroweak scale physics.

Proposed method

• Formulates a gravitational action with non-minimal coupling ξ between the Higgs field and Ricci scalar R, and a quadratic R² term (αR²) to generalize Einstein-Hilbert gravity.
• Performs a Weyl transformation to map the Jordan frame action into the Einstein frame, where gravity is standard and the Higgs field mixes with a new scalar field χ.
• Derives the effective potential in the Einstein frame, showing that the Higgs mass matrix becomes non-diagonal due to Higgs-Weyl mixing, leading to physical mass eigenstates h and H.
• Computes the physical Higgs coupling to SM particles as μ ≈ 1 − 6mₚ⁻²ξ²v², constrained by LHC data to |ξ| ≲ 10¹⁵ at 95% C.L.
• Evaluates the effective Higgs self-coupling λ_eff = 2λ_eff v², showing it increases with ξ due to quantum corrections from the αR² term.
• Derives the physical Higgs self-coupling as λ_h ≈ λ(1 − 12mₚ⁻²ξ²v²), showing enhancement over the SM value for large ξ, with perturbativity requiring |ξ| ≲ 10¹⁰.

Experimental results

Research questions

• RQ1 Can the electroweak vacuum metastability problem be resolved without introducing new particles or fine-tuning the initial Higgs value?
• RQ2 How does non-minimal coupling of the Higgs to higher-curvature gravity (αR²) affect the stability of the electroweak vacuum during and after inflation?
• RQ3 What are the observable consequences of Higgs-χ mixing on Higgs production and decay rates at colliders?
• RQ4 What constraints does the LHC data on the global signal strength μ impose on the non-minimal coupling parameter ξ?
• RQ5 To what extent can the physical Higgs self-coupling be enhanced beyond the Standard Model value, and is it within the reach of next-generation colliders?

Key findings

• The non-minimal coupling parameter ξ is constrained by LHC data to |ξ| ≲ 10¹⁵ at 95% confidence level, based on the global signal strength μ ≈ 1.07 ± 0.18.
• The physical Higgs self-coupling λ_h is enhanced over the Standard Model value due to quantum corrections from the αR² term, with λ_h ≈ 0.13 + mₚ⁻²α⁻¹ξ⁴v² for λ_eff ≈ 0.13.
• Perturbativity requires |ξ| ≲ 10¹⁰ to keep λ_h < 1, providing a tighter bound than cosmological or collider constraints alone.
• The mass of the heavy scalar state H (inflaton) is M ≈ mₚ(6α)⁻¹/² ≈ 10¹³ GeV, decoupled from low-energy physics.
• The physical Higgs mass is m_h² ≈ [2λ − ξ²/(2α) · (2mₚ⁻¹ξv)² / (1 + (2mₚ⁻¹ξv)²)]v², showing a non-trivial dependence on ξ and α.
• The model predicts a measurable deviation in the Higgs self-coupling from the SM, with λ_h > λ_SM for ξ ≳ 10¹⁰, making it testable at future colliders.