Cosmology from Two Axioms 16; Testing the Large-Scale Structure Imprint of Computational Hierarchy in Cosmic Evolution

This paper explores the fundamental question of whether cosmic evolution isconstrained by computational complexity hierarchies. We propose that if physical evolution processes are bounded by polynomial-time computability, then thegenerated large-scale structure density fields and the cosmic microwave backgroundradiation fields will carry specific ”complexity imprints.” By establishing a mappingframework from computational complexity theory (e.g., P, PSPACE classes) to cosmological observables, we derive quantitative predictions without free parameters:the evolution rate of the normalized compression ratio of the large-scale structuredensity field with respect to redshift is approximately dC/dz ≈ −1.0 × 10−3; thestatistical complexity of the primordial CMB temperature fluctuation field at redshift z ∼ 1100 exhibits a plateau feature of about 3.2±0.5 bits. This paper furtherproposes a double-blind testing methodology based on high-fidelity numerical simulations to establish a null hypothesis distribution. Utilizing observational data fromDESI, Planck, etc., and through complexity proxy measurements (such as losslesscompression ratio and causal state reconstruction), we test these predictions. Thisframework provides a clear falsifiable path for the hypothesis that ”cosmic evolution is computationally constrained,” representing the first systematically testablescheme at the intersection of computational complexity theory and observationalcosmology.