Cosmic Time Cosmology: Redshift from a Scalar Clock Field

This record provides a preprint of the manuscript “Cosmic Time Cosmology: Redshift from a Scalar Clock Field” CTC can be formulated as a two-metric theory in which: gravity is described by a gravitational metric (which admits a static background description in the cosmological setting considered), matter and electromagnetism couple to a matter metric that takes FLRW form in homogeneous backgrounds. the two metrics are linked by a homogeneous scalar clock field that controls how the matter metric evolves relative to the gravitational one., and from which the relation between gravitational proper time and matter-clock time follows. In homogeneous cosmological backgrounds, the observed redshift and time dilation arise because the matter metric—and therefore the physical time standard used to measure frequencies—changes over cosmic history, even if the gravitational spatial geometry is described in a static form. The theory is formulated covariantly from an action, leading to well-defined field equations and an exchange law between the matter sector and the clock field, and we outline the main background implications and avenues for observational tests. The theory is constructed within the scalar-tensor/Jordan-Einstein formalism and remain compatible with established local physics, including local Lorentz invariance, the equivalence principle, and standard microphysics. Version v2: added a reference within the introduction/ minor editorial update.