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 G₄₅₅ (H) and yields an exactly solvable expansion history. For the minimal infrared-enhanced entropy response, 1G₄₅₅ (H) =1G+4d S₎ₔₓd A, d S₎ₔₓd A H_²H² 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 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 (with =+). 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 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 A² correction to S₎ₔₓ, (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 CDM, and (d) a derivation of the (1+2H) “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.