Emergent Cosmology from Open Quantum Gravity: Exact Background Dynamics, Covariant Retarded Response, and Horizon-Localized

We develop a cosmological framework in which the observable universe is treated as an open gravitational system: inaccessible degrees of freedom (modes beyond the apparent horizon, coarse-grained environmental fields, or unobserved sectors) are traced out, generating a Schwinger–Keldysh influence functional with a retarded self-energy and a noise kernel. At the background level, the area derivative of the generalized horizon entropy defines an effective coupling $G_{\mathrm{eff}}(H)$ and yields an exactly solvable expansion history. For the minimal infrared-enhanced entropy response, $$ \frac{1}{G_{\mathrm{eff}}(H)}=\frac{1}{G}+4\frac{\mathrm{d} S_{\mathrm{out}}}{\mathrm{d} A},\qquad \frac{\mathrm{d} S_{\mathrm{out}}}{\mathrm{d} A}\propto \frac{H_\star^2}{H^2} $$ the modified Raychaudhuri equation integrates to a closed-form solution for $H(a)$ in terms of the Lambert $W$ function. At the perturbative level, we impose (i) ultraviolet recovery of General Relativity, (ii) infrared consistency with the background coupling, (iii) causality and passivity (retarded poles only in the lower-half complex $\omega$ plane), and (iv) minimality (single-pole/Debye relaxation). The resulting non-local response is localized into a closed system of ordinary differential equations via auxiliary polarization variables: a density-memory source $X$ and a slip source $\Xi$ (with $\Phi=\Psi+\Xi$). We give a covariant completion in terms of retarded non-local curvature invariants, demonstrate Bianchi protection at linear order by defining the modification through the gauge-invariant $\Delta_m$, and prove regular adiabatic super-horizon initial conditions. We then provide top-referee-facing benchmarks: (a) a microphysical toy-model motivation for the leading $A^2$ correction to $S_{\mathrm{out}}$, (b) an explicit covariant mapping that ties the background and perturbation sectors to the same retarded kernel, (c) a compressed BOSS DR12 BAO consistency check and distance-modulus comparisons against $\Lambda$CDM, and (d) a derivation of the $(1+2H\tau)$ “Hubble drag” term in the localized Debye equation. The decisive observational signatures are horizon-localized: (i) a two-plateau scale-dependent growth suppression with a fixed transition scale and ultraviolet $k^{-2}$ recovery, and (ii) a scale-dependent departure from an ISW–lensing null-test ratio confined to $q\equiv k/(aH)\sim 1$, enabling a direct probe of the environmental relaxation time.