Siavash Spacetime Dynamics (SSD): A Covariant Action Principle for Compact Matter-Induced Geometry Synthesis and the Resolution of the Dark Sector

Standard cosmology (ΛCDM) requires an invisible dark sector comprising 95% of the cosmic energy budget, alongside an escalating 5σ Hubble tension. Here, we present the complete, self-consistent mathematical formulation of Siavash Spacetime Dynamics (SSD), a covariant extension of General Relativity wherein the presence of matter under extreme compactness catalyzes the continuous synthesis of new spacetime volume. Derived strictly from a fundamental action principle, SSD introduces a dynamical scalar degree of free- dom Φ coupled non-minimally to gravity via Ω(Φ)R, while leaving the fundamental mat- ter action Sm minimally coupled to gµν. This guarantees strict conservation of baryonic energy-momentum (∇µT µν (m) = 0), exact preservation of the Weak Equivalence Principle, and complete absence of unobserved fifth forces on fundamental particles. The scalar field is driven by a localized partial differential equation sourced by the spatial distribution func- tional of compact remnants (Jsynth), naturally resolving the Cauchy initial-value problem via retarded Green’s functions. Cosmic scalar evolution is strongly overdamped by Hubble friction (3HΦ), preserving early-universe CMB and BAO power spectra. The compactness ˙ threshold C = GM/(Rc2 ) suppresses spacetime creation in weak-field regimes, yielding ex- act agreement with Solar System PPN bounds (γ − 1 < 10−10). On galactic scales, static remnant-sourced scalar profiles analytically generate flat rotation curves without particle dark matter, while late-time volume accumulation resolves the Hubble tension (Hlocal 0 = 73.0 vs. HCMB 0 = 68.2 km s−1Mpc−1 ). All 11 quantitative predictions derived from the theoret- ical action exhibit full concordance with current observational datasets.