[Paper Review] Higgs mass determined by cosmological parameters

R. K. Nesbet|ArXiv.org|Nov 25, 2008

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper proposes that the Higgs boson mass is not a fundamental parameter but is instead determined by cosmological parameters through conformal symmetry in gravitational and electroweak theories. By replacing the standard Higgs mass term with a coupling to the Ricci scalar R, the theory derives a dynamically small Higgs mass of approximately 1.81×10⁻³³ eV, consistent with cosmological data and implying that a large Higgs mass would falsify the model.

ABSTRACT

Postulating that all massless elementary fields have conformal scaling symmetry removes a conflict between gravitational theory and the standard model of elementary quantum fields. If the scalar field essential to SU(2) symmetry breaking has conformal symmetry, it must depend explicitly on the Ricci curvature scalar of gravitational theory. This has profound consequences for both cosmology and elementary particle physics, since cosmological data determine scalar field parameters. A modified Friedmann equation is derived and solved numerically. The theory is consistent with all relevant data for supernovae redshifts below $z=1$. The implied value of the cosmological constant implies extremely small Higgs mass, far below current empirical lower bounds. Detection of a Higgs boson with large mass would falsify this argument.

Motivation & Objective

• To resolve the conflict between conformal symmetry in quantum field theory and the non-conformal nature of the Einstein-Hilbert action.
• To explain the observed cosmological constant and dark energy as arising from the scalar field responsible for electroweak symmetry breaking.
• To derive a fundamental prediction for the Higgs boson mass from cosmological parameters rather than from the standard model's Higgs mechanism.
• To test whether the absence of a detectable Higgs boson can be explained by a dynamically small mass arising from conformal coupling to spacetime curvature.

Proposed method

• Postulate that all massless fields, including the Higgs doublet, possess conformal scaling symmetry, requiring the scalar field Lagrangian to include a coupling to the Ricci scalar R.
• Replace the standard Higgs mass term w²Φ†Φ with w²Φ†Φ − (1/6)RΦ†Φ to preserve conformal invariance, where R is the Ricci scalar from the Robertson-Walker metric.
• Derive a modified Friedmann equation from the conformal gravitational action, incorporating the scalar field's energy-momentum tensor and solving it numerically against supernova redshift data.
• Fit the model to observational data (e.g., Mannheim’s H₀d_L data) to determine cosmological parameters, including the effective cosmological constant Λ̄ = (3/2)w².
• Use the observed value of the cosmological constant (ΩΛ ≈ 0.726) to infer the effective w² and thus the Higgs mass m_H = √(2w²).
• Account for time-dependent R through the evolving scale factor a(t), leading to a weak coupling to the Z⁰ boson and a small effective Higgs mass in the current cosmic epoch.

Experimental results

Research questions

• RQ1 Can the Higgs boson mass be derived from cosmological parameters rather than being a free parameter in the standard model?
• RQ2 Does requiring conformal invariance in the gravitational and electroweak sectors lead to a consistent theory that explains dark energy?
• RQ3 What is the predicted value of the Higgs mass if the Higgs field couples to spacetime curvature via the Ricci scalar R?
• RQ4 How does the time-variation of R in an expanding universe affect the effective Higgs mass and its coupling to gauge bosons?
• RQ5 Would a large Higgs boson mass falsify the proposed conformal theory linking gravity and electroweak symmetry breaking?

Key findings

• The theory predicts a Higgs boson mass of approximately 1.81×10⁻³³ eV, derived from the observed cosmological constant and conformal coupling to the Ricci scalar.
• The model fits supernova redshift data (z ≤ 1) with a modified Friedmann equation, yielding ΩΛ = 0.732, consistent with the empirical value ΩΛ = 0.726 ± 0.015.
• The effective cosmological constant Λ̄ = (3/2)w² arises naturally from the scalar field's self-interaction via virtual Z⁰ boson exchange, linking dark energy to electroweak physics.
• The Higgs mass is not a fundamental parameter but is instead determined by cosmological evolution and the current value of the Hubble parameter H₀ ≈ 70.5 km/s/Mpc.
• A large Higgs boson mass (e.g., above a few GeV) would falsify the model, as it would contradict the predicted tiny mass from cosmological data.
• The theory explains the absence of a detected Higgs boson not as a failure of the standard model, but as a consequence of a dynamically small Higgs mass arising from conformal symmetry and spacetime curvature.