Expanse Tension Theory Hypothesis 3: The Holland–Higgs Field as a Single Scalar Unification of Mass, Gravity, and Cosmic Expansion.

The Holland–Higgs Field Theory: A Density-Dependent Unified Framework Linking Gravity, Inertia, and Cosmic Expansion

Abstract

This paper presents the Expanse Tension Theory (ETT) under Hypothesis 3, unifying the gravitational, inertial, and cosmological behaviours of mass through a single scalar field that couples the Standard Model Higgs mechanism to a new density-dependent field, denoted Φ (the Holland Field). The theory proposes that apparent gravitational attraction and cosmic acceleration both emerge from the modulation of mass–expansion coupling, governed by the local mass–energy density ρ and a phase-dependent “Holland–Higgs coupling efficiency”. A critical transition density, ρ₍c₎ ≈ 10⁻²¹ – 10⁻²² kg m⁻³, naturally arises from the covariant field equations, predicting the onset of galaxy rotation anomalies, star-formation cut-offs, and cosmic late-time acceleration—without invoking dark matter or dark energy. High-density symmetry restoration at ρ ≈ 10¹⁸–10¹⁹ kg m⁻³ provides the opposite transition, consistent with neutron-star phenomena and gravitational-wave observations. The framework retains full gauge invariance, reproduces the Newtonian limit, and matches the Standard Model in flat spacetime. This document consolidates the complete mathematical derivation, parameter definitions, and observational predictions of the ETT Holland–Higgs Field Theory v1.7 (Oct 2025).

Description

The ETT Holland–Higgs Field Theory extends earlier Expanse Tension Theory hypotheses by merging the Holland scalar field Φ—which defines expansion tension—with the Higgs scalar H of the Standard Model into a single covariant framework. It introduces a density-dependent effective potential

Veff(Φ,ρ)=−12μ2Φ2+14λΦ4+12ξρΦ2,V_{\mathrm{eff}}(\Phi, \rho) = -\tfrac12 μ^2 Φ^2 + \tfrac14 λ Φ^4 + \tfrac12 ξ ρ Φ^2,Veff(Φ,ρ)=−21μ2Φ2+41λΦ4+21ξρΦ2,

producing two field modes separated by a critical density ρc=μ2/ξρ_c = μ^2 / ξρc=μ2/ξ. Below ρ₍c₎, the “Holland mode” exhibits a double-well potential and long-range coherence, corresponding to the regime of galaxy-scale gravitational behaviour. Above ρ₍c₎, the “Higgs mode” collapses to a single-well potential, restoring conventional mass–field symmetry. This density-triggered duality yields a unified explanation for:

• Flat galaxy rotation curves and baryonic–dark matter scaling relations (SPARC data),

• Outer-disk star-formation thresholds,

• Late-time cosmic acceleration (LTA) as a coupling collapse at ρ ≈ 10⁻²⁷ – 10⁻²⁶ kg m⁻³,

• Neutron-star phase transitions and “glitch” phenomena via chiral-restoration coupling fall at ρ ≈ 10¹⁸–10¹⁹ kg m⁻³.

The paper details the covariant Lagrangian, field equations, and limiting behaviour across density regimes A–E, supported by analytic derivations, comparative observational tables, and a complete Reference 1 list to peer-reviewed scalar-tensor and Higgs-portal literature.

ETT v1.7 represents the culmination of the unified-field development cycle (2023–2025), merging gravitational, quantum, and cosmological domains under a single density-dependent scalar field. It is offered as a testable theoretical framework, not a claim of proof, inviting participation, replication, and peer review.