On the Temporal Structure of Cosmological Redshift and the Representational Status of Expansion

This paper analyzes cosmological redshift by isolating the invariant observational structure that precedes any spatial interpretation. Starting from the local definition of proper time and frequency in general relativity, we show that redshift is fully characterized by invariant relations between distinct local time scales, expressed through frequency ratios and the induced re-spacing of reception intervals along an observer’s worldline. This structure is purely temporal and does not invoke spatial distance, scale, or motion. We then examine how these temporal relations are reorganized into a spatial representation through the introduction of spacelike foliations and a scale factor in cosmological practice. The language of expansion is shown to provide an economical spatial encoding of temporally defined observational data rather than introducing additional invariant observables. The uniformity of cosmic expansion is traced to the uniform temporal registration inherent in observation. Finally, we delineate the limits of spatial interpretation and clarify the representational status of notions such as expanding space and superluminal recession.