Causal Structure Perspective on Cosmology: Curvature Coherence as a Structural Invariant

Abstract: We present a causal structure perspective on cosmology in which physical reality is described as a network of realizable relations evolving under constraints, rather than as a collection of isolated objects. A coarse-grained structural field, the causal cloud C(x,T), is introduced to represent the accumulation and distribution of these relations. Within this framework, spacetime geometry, thermodynamic irreversibility, and quantum correlations are interpreted as different manifestations of an underlying relational structure. We focus on the observable consequences of cumulative structural evolution in cosmological data. We introduce two model-independent quantities: the Relational Curvature Invariant (RCI) and the Sign-Coherence Statistic (SCS), which characterize the second-order structure of the distance modulus–redshift relation. The central prediction is that cosmic curvature exhibits sign coherence across the observable redshift range, indicating a structural invariant rather than a parameter-dependent feature. This prediction provides a falsifiable test: persistent curvature sign reversals beyond statistical fluctuation would challenge the framework, while sustained sign coherence across independent datasets would support the interpretation of curvature as an emergent consequence of cumulative causal structure. Rather than introducing new fields or modifying gravitational dynamics, this work identifies a structural observable that shifts the focus from parameter fitting to invariant patterns. This suggests that large-scale cosmological behavior may be governed by accumulated relational constraints. Significance: This work proposes a shift from parameter-driven cosmology toward structure-based observables. By identifying curvature coherence as a testable invariant, it offers a new approach to distinguish underlying physical structure from model-dependent fitting. The framework connects thermodynamic irreversibility, spacetime geometry, and quantum correlation within a unified relational interpretation, providing a potential pathway toward a more integrated understanding of physical reality.