This work presents Clockwork Cosmology, introducing Version 2.2 of the Temporal Rate Matrix (TRM) framework as a unified scalar-field approach to gravitational and cosmological phenomena. This version extends the initial release (Version 1) with a fully developed mathematical formulation and multi-domain validation. Instead of modeling dark matter and dark energy as separate physical components, the TRM framework interprets observed discrepancies as manifestations of a single dimensionless temporal rate field, T(x,t). In this framework, gravitational dynamics and cosmic expansion are described as kinematic effects arising from spatial gradients and global temporal drift of this field. The framework is evaluated across four independent observational domains: - Galactic rotation curves using the SPARC database - Galaxy cluster dynamics using the ACCEPT catalog - Cosmic Microwave Background acoustic scales using Planck data - Type Ia supernova luminosity–distance relations using the Pantheon+ dataset Across these domains, the TRM framework reproduces key observational features through domain-specific boundary conditions derived from the same scalar field, providing a unified interpretative structure. This work is presented as a testable theoretical framework rather than a finalized cosmological model. It explores whether temporal-rate dynamics can contribute meaningfully to the interpretation of large-scale structure and cosmic evolution. All source files and numerical approaches are provided to support independent verification and further development. *** Note on AI Assistance: Generative artificial intelligence tools (including Gemini and OpenAI GPT models) were used to assist in refining the linguistic phrasing and clarity of the manuscript, as well as supporting the formatting of mathematical expressions. All core physical concepts, derivations, and conclusions were developed solely by the author, who assumes full responsibility for the content.
Fabrice Wieser (Sat,) studied this question.