Ringdown Gravity: A Self-Contained Effective Gravitational Theory of the Dark Sector

Abstract

Ringdown Gravity (RG) is a self-contained effective gravitational theory of the dark sector in which phenomena conventionally attributed to dark matter and dark energy arise from the response of a ringing horizon rather than from a new dark particle. The paper develops the fixed-background foundation directly within the manuscript. In the axial \(\ell=2\) Schwarzschild sector, a canonically normalized horizon distinguishability functional is shown, after an affine horizon map, to coincide algebraically with coherent modular relative entropy, \(D_H=S_{\rm rel}\). For an exact single pole, the information decays at twice the field damping rate. The construction is extended to stationary non-extremal Killing horizons, where rotation and charge modify the horizon generator and canonical flux but not the affine future kernel. Version 2 develops the effective relativistic closure further. The timelike direction \(A^\mu\) is treated as a state/algebra-derived readout rather than as an independently varied vector or aether field. The local branch coordinate is reconstructed from relative history content, and the induced metric variation, history-current exchange and Ward/Bianchi identity are obtained within a single one-metric diffeomorphism-invariant effective framework. The theory contains the radial-acceleration relation \(a=\sqrt{g_N(g_N+a_0)}\), a spatial kinetic sector \(F(Y)\propto Y^{3/2}\), a pressureless history component with cold-dark-matter-like linear perturbations, and a minimal dark-energy sector with \(w_0\approx-0.986\). The local nonlinear response is survival-screened at high acceleration. Version 2 also gives the exact static spherical exterior equations and their relativistic matching. In the screened Solar-System regime the standard polynomial PPN coefficients reduce to \(\beta=\gamma=1\), while the remaining branch-dependent vacuum-curvature residue is of order \(a_0^2/c^4\) and is negligible for planetary dynamics. The accompanying reproducibility package includes the background/CAMB calculation, a public Regge-Wheeler time-domain reference solver, and the spherical/state-readout numerical checks. At background and linear-CMB level, RG is nearly degenerate with \(\Lambda\)CDM. Its main nonlinear discriminator is structural rather than tied to one numerical benchmark: \[ R_{\rm void}=\frac{1}{R_c}<1\qquad (R_c>1). \] Using the benchmark \(R_c=1.90\) gives \(R_{\rm void}\approx0.526\). A robust measured void dynamical-to-baryonic ratio at or above unity would therefore falsify the present correspondence rule. Included files:Ringdown_Gravity_v2.pdf — manuscriptRingdown_Gravity_Zenodo_v2_2026_Updated.zip — reproducibility package, source code, numerical outputs, documentation and checksums Correspondence: kaya@cab-film.com