Coordinate Density Field Theory (CDFT): A Split-Metric Scalar Compression Framework for Gravity

### AbstractCoordinate Density Field Theory (CDFT) encodes the static gravitational sector and homogeneous cosmology in a single dimensionless field φ(x) defined on a Minkowski reference, with operational intervalsds²_phys = e-2φ c² dt² − e+2φ dx².For sourcing/variation only, matter couples universally to g̃μν = e+2φ ημν, yielding the trace-sourced equationβ □φ + dV/dφ = T with β = c⁴/(4πG) > 0 on a vacuum-subtracted, flat-minimum (Yukawa-free) weak-field branch.The weak-field expansion gives γ_PPN = β_PPN = 1 in the static isotropic sector.In the baseline non-spinning exponential exterior, the photon-ring (shadow) diameter is a +4.6% benchmark relative to Schwarzschild at fixed (M, D), and in the adopted compact-object construction an absorbing boundary at r_h = 2GM/c² implies no long-lived echoes.Assuming the static interior depends only on the relative compression Δφ = φ − φ_∞ (i.e. invariance under constant background shifts), compact-object sensitivities vanish (s_A = 0), eliminating scalar dipole radiation; the leading scalar channel is quadrupolar and is suppressed relative to GR by EOS/trace and wave-zone factors.Cosmologically, a Λ-free FRW branch admits late-time acceleration as a boundary-fixed integration mode in H(a); for late-time sub-horizon checks we provide a GR-emulator dictionary under explicit dust/no-slip/Poisson closures.Galaxy phenomenology is implemented via a phenomenological one-scale μ-law with the FRW-fixed a_0(z) = cH(z)/(2π) and is confronted with SPARC/BTFR/RAR catalog-level tests.A uniform local-domain offset φ_loc rescales ladder distances, producing an apparent H₀ split without changing the global H(z). ### Files- `CDFT.pdf` — compiled preprint- `CDFT_source_v1.zip` — LaTeX source + prebuilt bibliography (`CDFT.bbl`) + README ### Build (source ZIP)This source package compiles without running BibTeX (the bibliography is included as `CDFT.bbl`).Run:- `pdflatex CDFT.tex` (twice; a third time only if LaTeX asks to rerun for cross-references) ### Keywordsgravitation; alternative theories of gravity; quantum gravity; scalar field; cosmology; compact objects; post-Newtonian tests ### How to citeAwdhoot, T. (2026). *Coordinate Density Field Theory (CDFT): A Split-Metric Scalar Compression Framework for Gravity* (Version v1). Zenodo. https://doi.org/10.5281/zenodo.18624273