The Flux–Shadow Gravity Model: A Unified Alternative to Dark Matter

We propose The Flux–Shadow Gravity Model, a gravitational framework in which apparent gravity arises from a single dark-energy–driven expansion flux (i.e., the standard FLRW/Hubble expansion-flow of spacetime, expressed kinematically—not a particle or material flux) rather than from a fundamen- tal force of attraction. In this formulation, cosmic expansion establishes a background outward flux of spacetime, and baryonic matter partially obstructs this flux. The resulting flux asymmetry pro- duces a geometric acceleration toward obstructing regions, reproducing the phenomenology ordinarily attributed to gravitational pull without postulating an underlying attractive interaction. Flux obstruction generates a nonlocal shadow field that modifies the gravitational potential of ex- tended baryonic distributions while vanishing (by construction) for an isolated spherically symmetric source in its exterior field. As a consequence, isolated spherical bodies produce no shadow monopole, so their exterior field obeys the standard Newtonian 1/r2 acceleration law and remains consistent with Solar-System weak-field constraints (and, for near-spherical compact bodies, shadow corrections are strongly suppressed in the regimes probed by standard weak-field tests), whereas disks and other non-spherical systems generate a logarithmic tail that behaves like a diffuse halo. Extended quasi-flat (slowly declining) galactic rotation-curve plateaus over the observed radial window, enhanced weak lensing, and cluster-scale mass discrepancies are therefore explained by baryon-induced flux shadows rather than particle dark matter. Wea) express the theory in terms of an effective covariant action and a nonlocal shadow operator B acting on the baryon distribution, yielding in the quasi-static weak-field limit the modified Poisson equation ∇2Φ = 4πG(ρb + B[ρb]) ≡ 4πG(ρb + B), where ρb is the baryon density and B ≡ B[ρb] is the resulting geometry-dependent shadow density. In the quasi-static weak-field regime, the model is constructed to recover standard GR light- propagation effects (light bending, Shapiro delay, gravitational redshift) in spherical systems, with the shadow entering only through the effective source term; within the same weak-field treatment, post-Newtonian parameters and gravitational-wave propagation reduce to their GR forms, with the shadow entering only as an additional effective density term. On cosmological scales, the spatially averaged shadow behaves as a pressureless component with den- sity parameter Ωflux, and can be mapped onto the role of Ωcdm in standard ΛCDM analyses at the level of linear cosmology. Numerical tests using the CLASS Boltzmann code demonstrate phenomenological compatibility with CMB acoustic peaks and large-scale growth when the spatially averaged shadow contribution is treated as an effective pressureless component. This should be understood as an effec- tive equivalence test, not as a completed derivation of the kernel-evaluated shadow field through the tightly coupled pre-recombination plasma. As a representative application, we demonstrate—using a multi-galaxy SPARC disk sample—that the thin-disk projection of the geometric shadow kernel pro- duces realistic rotation curves using only the observed baryons, consistent with the broader class of disk-galaxy tests discussed in this work. The model also predicts that effective halos should tightly correlate with baryonic geometry, that truly baryon-free lenses should not exist, and that cluster lens- ing asymmetries should depend on compactness rather than total baryonic mass, providing multiple avenues for near-term falsification. Here and throughout this work, the term “dark matter” refers specifically to particle dark mat- ter as conventionally assumed in ΛCDM. The present framework does not eliminate the dark-matter phenomenology required by cosmological observations, but replaces particle dark matter with an effec- tive, baryon-linked flux–shadow contribution that reproduces the same gravitational and cosmological signatures within its stated domain of validity. In this framework, time is interpreted as tracking the global flow of cosmic expansion, mass represents local obstruction to that flow, gravity emerges as a flux–shadow effect generated by geometric suppression of expansion, and rotational or orbital motion arises as angular equilibrium within the anisotropic expansion field.