Emergent Cosmological Dynamics from Stochastic Bidirectional Causality: A Unified Extension of ΛCDM

We introduce the Stochastic Bidirectional Causality (SBC) model, a relational and memory-driven extension of ΛCDM in which cosmological observables emerge hierarchically from non-Markovian, temporally correlated dynamics. Unlike conventional models that assume immutable universal parameters, SBC posits that quantities such as the Hubble constant (H 0) and the structure growth parameter (S 8) arise as statistical expectations conditioned on the observer’s causal accessibility. The mathematical foundation of the model is built upon generalized stochastic Friedmann equations and norm-preserving evolution laws modulated by memory kernels. These encode both past fluctuations and ensemble-level statistical constraints without invoking retrocausal signaling. The resulting architecture generates a structured form of physical dispersion, in which observable variance is not experimental noise but a signature of stochastic causal depth. Empirical validation proceeds hierarchically: from highly constrained primor-dial spectra (C T T ℓ , C EE ℓ) to intermediate observables (H(z), f σ 8 (z)), and finally to context-sensitive parameters like H 0 and S 8. Applied to current cos-mological datasets (Planck, SH0ES, DESI, KiDS, Pantheon+), the SBC model yields emergent ensemble values of H 0 = 70.1 ± 1.1 km s −1 Mpc −1 and S 8 = 0.790±0.021, outperforming both ΛCDM and Early Dark Energy (EDE) in joint fits across all observables under equal or fewer degrees of freedom. All results are fully reproducible from open-source Jupyter notebooks. SBC thus offers not only a novel theoretical framework, but a transparent, falsifiable and epistemologically grounded approach to cosmic inference.