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 Geff(H) and yields an exactly solvable expansion history. For the minimal infrared-enhanced entropy response, 1Geff(H)=1/G+4d Sₒᵤₜd A, d Sₒᵤₜd A∝ H_²/H² 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 ω 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 Ξ (with Φ=Ψ+Ξ). 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 Δₘ, and prove regular adiabatic super-horizon initial conditions. We then provide top-referee-facing benchmarks: (a) a microphysical toy-model motivation for the leading A² correction to Sₒᵤₜ, (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 ΛCDM, and (d) a derivation of the (1+2Hτ) “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≡ k/(aH)~ 1, enabling a direct probe of the environmental relaxation time.