A Falsifiable Roman-Era Program for Coherence-Driven Cosmology: Unified Predictions from the ToE-2PS Framework

This work presents a unified, falsifiable observational program for testing environment-dependent cosmology using next-generation data from the Nancy Grace Roman Space Telescope. Building on the ToE-2PS cosmology framework, we integrate four key predictions into a coherent analysis strategy: (i) an environmental step in Type Ia supernova distance moduli (VoidStep-H0), (ii) mild dynamical evolution of the dark energy equation of state, (iii) the existence of a structured deviation field relative to ΛCDM, and (iv) a nonzero correlation between this deviation field and the large-scale matter density distribution. We introduce a minimal parameterization of the expansion rate that incorporates both late-time homogeneous modulation and weak environmental dependence. From this, we define a generalized observable, λ_cosmo(x,z), capturing deviations between observations and ΛCDM predictions across multiple probes, including luminosity distances, weak lensing, and clustering-derived quantities. A three-phase analysis pipeline is proposed and fully specified: (1) environmental classification of supernovae (voids vs filaments), (2) reconstruction of the residual field λ_cosmo(x,z), and (3) cross-correlation with the matter density field δ_m. Each phase is associated with explicit statistical metrics (KS test, PCA, correlation coefficients, and power spectra) and well-defined falsification criteria. The program is designed to leverage Roman’s unique combination of survey depth, sky coverage, and multi-probe capability, enabling percent-level tests of structured deviations from ΛCDM. Importantly, the framework is explicitly falsifiable: null results would significantly constrain the class of environment-dependent cosmological models, while positive detections across multiple probes would provide strong evidence for a new observational regime in late-time cosmology. This work therefore establishes not only a theoretical extension, but a concrete and testable pathway toward determining whether cosmic expansion is purely homogeneous or weakly modulated by large-scale structure.