Relativity and Cosmology

   

Space-Clock Field Theory: A Single Metric Candidate for Dark Sector Unification

Authors: Mauro Alfonso Montenegro

Spacetime is conventionally treated as a four-dimensional background within which matter and gravitational phenomena occur. Space-Clock Field Theory (SCFT-A) advances a field-first alternative: the Lorentzian metric is the gravitational field, and physical space is the clock-orthogonal spatial state of that field, rather than an independent background container in which gravity resides. A dynamical scalar clock T selects the physical foliation and distinguishes cosmological clock-field time T from matter proper time t, the invariant time measured along material worldlines. Along homogeneous clock-comoving trajectories, the two physical times satisfy dT= Q dt, so that NT → dt/dT= Q→1 and HT = H/Q. Because T carries stress, conjugate momentum, conserved charge, and gravitational backreaction, this distinction changes relational observables and cannot be removed by a coordinate transformation. The theory’s central reciprocal statement is: As physical space expands, cosmological time contracts or moves slower; as physical space contracts, cosmological time expands or moves faster. The expanding branch obeys the on-shell response dNT /dH < 0. An explicit unbraided contracting branch has˙ Q > 0; this clock-rate statement has a different response sign and is proved only on its stated branch. This gravitational—clock architecture motivates the proposed extended equivalence principle, gravity= proper acceleration= physical space= relativistic aether= vacuum, where= denotes identity of physical sector rather than mathematical equality among curvature, acceleration, spatial geometry, causal structure, and vacuum states. SCFT-A realizes these principles using one universally coupled metric and one shift-symmetric scalar clock. The same operator family admits specified approximately matter-like regimes, a late self-accelerating endpoint, and a controlled local stationary MOND/AQUAL operator limit, without a separate cold-dark-matter action, dark-energy fluid, bare cosmological constant, or second matter metric. These are classical branch results, rather than a completed dark-sector unification theorem. A convex kinetic interpolation and positive spatial derivative operators define a deliberately constructed classical example. An explicit revised coe"cient point, ωm/H2 d = 1030 , ε = 10→140 and ϑ = 10→6, replaces uncertified numerical extrema by proved su"cient bounds. It preserves all-momentum local scalar positivity and a positive tensor spectrum. A generalized endpoint polynomial proves positive scalar kinetic and restoring coe"cients, and an exact decreasing energy controls every endpoint scalar mode despite redshifting momentum. The revised stationary correction ratio is strictly below 10→14 at a declared subhorizon scale. (Truncated to < 400 words by viXra Admin)

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[v1] 2026-09-15 20:48:48

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