A Null Test of Scale–Time Coupling in Cosmological Structure Formation

This work presents a conceptual framework for testing the separability assumption in cosmological structure formation. We introduce a mixed-derivative diagnostic of the matter power spectrum that vanishes identically for separable scale and time evolution, and therefore serves as a null test for scale–time coupling. The approach is model-independent and is motivated by scenarios in which time-dependent clustering properties of dark energy induce a drifting characteristic scale in large-scale structure. The work is exploratory in nature and is intended as a theoretical consistency proposal rather than a predictive model. This manuscript was developed with the assistance of large language models for conceptual exploration and drafting support.