Vacuum energy and asymptotic freezing of a composite Planck field in a gauge-invariant scalar cosmology
We study a classical complex scalar theory with the composite field ℏ(x) = β|ϕ(x)|, where β > 0 is constant. The ratio m/β fixes the vacuum energy density u0 = m2c2/β2 and, on an expanding, spatially flat, fluid-free branch with m > 0 and zero bare cosmological constant, the asymptotic Hubble rate H∞ = √[8πGNm2/(3β2)]. In this solution, ℏ approaches a finite constant without an amplitude-stabilizing potential. The scalar carries charge under an independent U(1) with a scalar-dependent gauge transformation and invariant field strength. The identity ℏ = β|ϕ| converts the nominal mass term into u0, and minimal coupling to Einstein gravity gives ΔΛ = 8πGNm2/(β2c2). On the homogeneous, isotropic background, a real scalar gauge and the vector equation imply Aμ = 0 and ℏ̈ + 3Hℏ̇ = 0. The vector retains a nonzero quadratic mass term in the constant-ℏ limit, even though the exact cosmological solution has Aμ = 0. We map the background to scalar-plus-vacuum cosmology and distinguish this action from varying-coupling and dilaton precedents. An inflaton extension shows rapid gravitational damping of the Planck-field velocity, while direct potential coupling can sustain its growth. The vacuum term is algebraic; freezing is dynamical. Neither the observed constants nor a universal quantum interpretation of ℏ is established.
Authors
- Rand Dannenberg
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-06
- DOI
- https://doi.org/10.5281/zenodo.23192338
- Primary Topic
- Cosmology and Gravitation Theories
- Type
- preprint