A Temporal Calculus: Conformal Scalar-Tensor Formulation, Laws, Cosmology, Binary Pulsars, and Observational Fits

Within the Chronoflux Research Initiative I construct a covariant temporal calculus in four dimensions in which a positive scalar field τ determines the physical metric through the conformal relation g̃ = τ⁻² g. Variation of the action produces Einstein equations for the metric together with a sourced scalar wave equation, while matter follows geodesics of the physical metric. In the weak field limit the dynamical law becomes a = −c² grad ln τ, reproducing Newtonian gravity with potential Φ = c² ln τ.

The theory can be written in scalar–tensor form, allowing direct comparison with solar-system tests, optical clock measurements, binary pulsar timing, and cosmology. General relativity appears as the equilibrium solution when the scalar field is constant, while slow evolution of the scalar potential produces accelerated expansion consistent with Planck 2018 constraints. Bounds on the coupling and scalar mass are obtained from Cassini tracking, post-Newtonian limits, and pulsar timing, yielding a restricted parameter region compatible with current observations.

All equations are formulated strictly in four dimensions and derived from a single action with consistent physical units. The resulting temporal calculus provides the scalar sector underlying later Chronoflux dynamical models and establishes a unified framework connecting Newtonian gravity, general relativity, scalar–tensor corrections, and cosmological acceleration.