The GETT Covariant Scalar-Density Framework for Emergent Gravity and Cosmology.

Author: John Edward Holland   ORCID: 0009-0001-5120-8712
© Copyright. John Holland.  All rights reserved.
Email:  john.holland@expansetension.org    Date: 15^th March 2026

General Expanse Tension Theory (GETT) Covariant Action Construction, Field Equations, Density-Regulated Interaction Structure, and Astrophysical Tests.

This paper establishes, for the first time in the literature, a fully covariant effective field theory in which a gauge-invariant singlet scalar field couples to all Standard Model matter through a Higgs-sector portal whose interaction strength is continuously and covariantly modulated by the local baryonic density – a construction that unifies the gravitational behaviour of cosmic voids, galactic discs, stellar interiors, and neutron star cores within a single density-regulated scalar mechanism, and in doing so offers not an alternative to General Relativity but its derivation as the inevitable, emergent, mid-density limit of a more fundamental field-theoretic reality.

The framework is formulated explicitly within the language of relativistic quantum field theory and effective field theory. The theory introduces a universal scalar field, Φ, constructed as a real gauge-invariant singlet that interacts with the Standard Model through a Higgs-sector portal. The strength of this interaction is regulated by a continuous modulation function S(Σ)S(\Sigma)S(Σ), where Σ\SigmaΣ is a covariant scalar constructed from the stress–energy tensor and represents the coarse-grained environmental baryonic density.

This density-regulated interaction structure naturally produces a hierarchy of dynamical regimes across the Universe. In mid-density environments such as terrestrial laboratories, planetary systems, and stellar interiors, the scalar coupling is strongly suppressed and the framework reduces smoothly to General Relativity coupled to the Standard Model. In lower-density astrophysical environments the scalar interaction becomes increasingly active, potentially influencing galactic rotation behaviour, vertical stellar kinematics, gravitational lensing in cosmic voids, and the growth of large-scale structure. At sufficiently extreme densities, such as those encountered in neutron star interiors or black hole formation regimes, the framework predicts additional scalar activation domains associated with symmetry restoration phenomena.

The theoretical construction preserves the core symmetry principles of modern physics, including general covariance, local Lorentz invariance, and Standard Model gauge invariance. The theory is expressed through a covariant action and Lagrangian formulation, from which the corresponding field equations are derived via standard variational principles. The resulting scalar–matter interaction provides a consistent effective field-theoretic description in which gravitational phenomena arise from density-regulated scalar coupling rather than from a purely geometric spacetime curvature alone.

The paper further outlines observational and experimental tests of the framework across multiple astrophysical environments. These include galaxy rotation curves, vertical stellar velocity dispersion measurements, gravitational lensing in cosmic structures and cosmic voids, large-scale structure surveys, cosmological expansion behaviour, and compact-object astrophysics. Several of these domains have already been investigated within the broader General Expanse Tension Theory (GETT) research programme using independent observational datasets, including analyses of the SPARC galaxy database and Gaia DR3 stellar kinematics.

This work forms part of the broader GETT research programme, which investigates the possibility that gravitational behaviour, inertia, and temporal dynamics emerge from density-regulated scalar–matter interactions within a unified field-theoretic framework. In this programme, classical gravitational laws are recovered as limiting cases through a structured correspondence analysis across density regimes.

The present paper therefore serves as the foundational field-theoretic formulation of the GETT scalar–density framework, establishing its mathematical structure, symmetry consistency, and observational implications. Subsequent papers in the programme investigate empirical tests of the theory across galactic dynamics, cosmological observations, and compact-object physics.

All source materials and related research outputs are available through the author’s Zenodo archive and associated publications.