Causal Automaton Spacetime II: Cosmological Perturbation Theory, Planck Likelihood Constraints, and Cellular Regularization Signatures

NOTE ON COMPANION RESEARCH SERIES: This manuscript constitutes Part II of the two-part Causal Automaton Spacetime (CAST) research programme, focusing on cosmological perturbation theory, linear Einstein-Boltzmann numerical integration (CAMB), and Planck 2018 Bayesian MCMC likelihood validation. The underlying axiomatic microstate foundations, causal topology, quantum spin correlations, and emergent gravitational field equations are established in the companion paper, Part I (Zenodo DOI: 10.5281/zenodo.23743449). --- Abstract & Empirical Validation Summary We investigate the cosmological perturbation phenomenology and observational likelihood validation of Causal Automaton Spacetime (CAST), confronting the discrete cellular network framework established in Part I against high-precision cosmological data. In the infrared regime (λ >> l_cell), the framework strictly recovers continuous General Relativity and the standard unperturbed ΛCDM expansion history. In the ultraviolet regime approaching the fundamental cellular regularizer (l_cell = 2√(ln 2) l_P ≈ 2.6914 × 10⁻³⁵ m), 3D Brillouin zone lattice dispersion coupled to Mukhanov-Sasaki Riccati-Bogoliubov vacuum mode emergence yields an isotropic effective transfer kernel T_CA(u) ≈ 1 - (π²/40) u² (where u = k/k_c) and a modified primordial curvature perturbation spectrum:P_R(k) = P_0(k) [1 - ξ_cast (1 - T_CA²(k / k_c))] Key Computational & Empirical Results in Part II: 1. Boltzmann Hierarchy & Astrophysical Landau Smearing:Full line-of-sight numerical integration through the modified CAMB Einstein-Boltzmann differential hierarchy demonstrates that finite Last Scattering Surface (LSS) visibility thickness (Δχ_rec ~ 150–250 Mpc) acts as a natural projection low-pass filter, smearing out microscopic high-frequency oscillatory mode ringing while preserving a monotonic power suppression across the acoustic damping tail as the robust observational signature. 2. Planck 2018 Bayesian MCMC Likelihood Validation:We confront the extended parameter space with the complete legacy cosmological dataset from the Planck 2018 satellite mission (plik_lite TT,TE,EE + low-l Commander/SimAll) using the Cobaya MCMC infrastructure across 4 independent chains reaching 37,091 accepted samples (N_eff = 25,347, Gelman-Rubin convergence R - 1 = 0.0291 < 0.03). 3. Global Likelihood Improvement (Δχ² ≈ -13.02):In the unconstrained exploratory run (N_par = 8), the minimum-variance best fit yields -ln L_min = 463.18758 (χ²_total = 1002.855), achieving a decisive global likelihood improvement of Δχ² ≈ -13.02 over baseline ΛCDM (χ²_ΛCDM = 1015.88). The improvement is driven by mitigating high-multipole acoustic tail power tension in the plik likelihood (Δχ²_plik ≈ -11.9). 4. Ab-Initio Concordance Without Post-Hoc Tuning (0.15σ):The marginalized posterior coupling ξ_cast = 0.05498 ± 0.03366 places the ab-initio theoretical prediction derived from boundary stereology (ξ_theory ≈ 0.050) within a 0.15σ concordance core, confirming physical grounding without empirical fine-tuning. 5. Parameter Orthogonality & Calibration Rigidity:Standard cosmological parameters remain strictly orthogonal to the cellular modifications: H_0 = 67.32 ± 0.60 km/s/Mpc, Ω_b h² = 0.02239 ± 0.00015, and Ω_c h² = 0.12005 ± 0.00136 remain unperturbed, while the instrumental calibration parameter is locked to unity at A_planck = 1.00054 ± 0.00249. General Relativistic lensing is strictly conserved (A_L ≡ 1). 6. Bayesian Model Selection Support (ΔBIC ≈ -5.0):In the predictive physical framework with theoretically fixed boundary coupling (N_par = 7), the single-parameter extension governed solely by the spatial cutoff scale k_c = 0.370 ± 0.136 Mpc⁻¹ achieves decisive information criteria support:ΔAIC ≈ -10.8, ΔBIC ≈ -5.0constituting strong statistical evidence favoring the CAST cellular regularizer over baseline continuous ΛCDM. 7. Popperian Null Falsification & Observational Forecasts:Projecting comoving modes to angular multipole space maps the lattice regularizer cutoff to l_c ~ 5180 (1σ range: l in [4100, 8350]), defining a quantitative, falsifiable Popperian benchmark directly accessible to forthcoming high-resolution bolometric surveys including CMB-S4, the Simons Observatory, and SPT-3G. ---Open-Source Computational Pipelines Included:The manuscript provides five complete, machine-verified Python and YAML validation pipelines in Appendices A.1–A.5:• Appendix A.1: Fourth-Order Runge-Kutta Riccati-Bogoliubov Solver• Appendix A.2: 3D Brillouin Zone Density of States Simpson Integrator• Appendix A.3: Standalone Production CAMB Boltzmann Integration Pipeline• Appendix A.4: Vectorized Cobaya Boltzmann Theory Component (cast_theory.py)• Appendix A.5: Production Cobaya MCMC Likelihood Specification (cast_mcmc_run.yaml) ---Manuscript Details:• Author: Dev S. Patel (Premise House / Independent Researcher)• Classification: Observational Cosmology / Primordial Perturbations / CMB• Target Journal: Journal of Cosmology and Astroparticle Physics (JCAP)• Code Repository: https://github.com/dev-s-patel• Companion Paper (Part I): Zenodo DOI: 10.5281/zenodo.23743449