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

We construct a testable cosmological model from \emph{open} quantum gravity: the observable patch is treated as an open system coupled to inaccessible environmental degrees of freedom beyond the apparent horizon. Tracing out the environment in the Schwinger--Keldysh formalism generates a causal influence functional with dissipation and noise kernels, leading to an Einstein--Langevin description. At the homogeneous level, we define the effective coupling by the area derivative of the generalized horizon entropy, $G_{\rm eff}^{-1}(H)\equiv G^{-1}+4\,dS_{\rm out}/dA$. After renormalizing the leading area law into $G$ and enforcing early-time GR recovery, the leading infrared contribution in a minimal analytic expansion is $dS_{\rm out}/dA\propto H_\star^2/H^2$, supported by both EFT and microscopic horizon-correlation arguments. The resulting background admits an exact analytic solution $H(a)$ in terms of the Lambert $W$ function and approaches a future de~Sitter fixed point without local ghost fields. At the perturbative level, UV recovery, IR matching to $G_{\rm eff}(H)$, causality/passivity, and model minimality motivate a single-pole (Debye) retarded kernel as the baseline benchmark; we also provide the multi-pole extension and ODE localization. Introducing auxiliary polarization variables $(X,\Xi)$ localizes the non-local memory into a manifestly causal ODE system that preserves Bianchi identities by construction and admits regular adiabatic super-horizon initial conditions. We derive observational templates: two-plateau growth suppression with transition scale $k_{\rm trans}(a)=a\sqrt{H^2+\beta}$ and UV $k^{-2}$ recovery, plus a horizon-localized bend in the ISW--lensing null-test ratio that probes the relaxation time. We also give a stochastic completion with fluctuation--dissipation relations. A full Einstein--Boltzmann computation in synchronous gauge reveals that for $b\simeq 0.07$--$0.10$ the model suppresses the CMB temperature quadrupole by $5$--$6\%$ while perturbing the acoustic peak amplitudes by less than $1\%$, naturally reproducing the direction and morphology of the observed Planck low-$\ell$ power deficit. A joint fit using DESI Data Release~1 BAO, Planck~2018 compressed distance priors, and Pantheon+ supernovae with the full supernova covariance confirms that the preferred background remains close to $\Lambda$CDM and does not exclude the $b$ range favored by the low-$\ell$ analysis. Within the allowed range the model predicts a characteristic scale-dependent suppression of the matter power spectrum localized to $k\lesssim 10^{-2}\,h\,$Mpc$^{-1}$. The predicted $S_8\equiv\sigma_8\sqrt{\Omega_{m0}/0.3}$ is expected to remain consistent with the Planck CMB value; we show that the gravitational slip parameter $\lambda$ is observationally unconstrained by current and planned surveys because its signature is localized to horizon scales. Numerical-analysis scripts and Boltzmann-solver implementation formulas are provided to support reproducibility, with full-likelihood release products deferred to future work.