Standard FLRW cosmology extrapolates observed cosmic expansion backward to a (t) ->0, producing a Big Bang singularity at finite proper time. This paper demonstrates that this singularity is a reconstruction artifact of imposing a globally isochronous expanding-frame description on a conformal temporal geometry. In the Temporal Equivalence Principle (TEP), the observational role of FLRW expansion is reconstructed through conformal temporal transport: the effective scale factor aₑff arises from accumulated open-path conformal temporal shear along cosmological lines of sight rather than from physical expansion of space. TEP-C0 (Paper 26) established the distance-redshift and supernova evidence and deferred full nonsingular matter-frame closure to a dedicated temporal-horizon analysis; here that closure is delivered. The Temporal Horizon Cosmology framework is developed here, proving that the apparent aₑff->0 limit is not a physical curvature singularity but a temporal horizon. Two distinct projections of the temporal field are required: Aclock (z) = (1+z) ^ (-1) is the exact observational clock/redshift mapping that drives aₑff->0 as z->infinity, while Adyn (z) = (1+z/zₜ) ^ (-epsilonₑff (z) ) is the dynamically screened shear response that modifies expansion, BBN, recombination, and perturbations only at late times. Proposition 1 establishes curvature regularity of the temporal conformal boundary: for Aclock (eta) =C eta^ (-p) with 0 0 and curvature invariants vanish. The conformal compactification is smooth, the Weyl tensor vanishes on the boundary, and every causal curve approaches the regular past boundary T^- rather than terminating at a singularity. The temporal horizon is therefore simultaneously curvature-empty, timelike-complete, and null-complete in this branch. The effective stress-energy tensor of the temporal field violates the Strong Energy Condition, an explicit prerequisite of the Hawking-Penrose singularity theorems. The thermal screening scale is Tₗock=0. 03 eV with transition redshift zₜ=100 and T₀=2. 725 K, giving strong epoch-by-epoch screening (Sₑpoch~10^-12 at BBN, ~10^-2 at recombination). Screened TEP reproduces the standard BBN successful sector and inherits the standard lithium anomaly. Recombination is computed with the full non-equilibrium Peebles/RECFAST treatment. The temporal-horizon thermal mapping preserves a FIRAS-compatible blackbody with no spectral distortions. The scalar perturbation spectrum is derived from fluctuations of the clock field, zeta=delta ln Aclock, yielding a power spectrum Pᵦeta (k) proportional to k^ (nₛ-1) with spectral-flow parameter nₛ-1=-2 epsilonfield. The observed Planck value nₛ=0. 965 constrains epsilonfield=0. 0175. Tensor modes are derived directly from the temporal-conformal metric: for Aclock (eta) ~eta^ (-p) the tensor source term Aclock''/Aclock=p (p+1) /eta²->0 at the horizon, so the tensor equation approaches the Minkowski vacuum. The imported inflationary consistency relation r=16 epsilonfield is not assumed. Numerical integration of the native tensor equation across the finite transition profile yields r (kₚivot) =9x10^-6 and rₘax=6. 26x10^-4, both well below the BICEP/Keck 2021 bound r<0. 036; tensor power is controlled only by the finite transition region. CMB anisotropy and LSS observables are reproduced in the screened-limit reduction, inheriting agreement with Planck 2018 and BOSS DR12 by construction rather than as independent empirical confirmation. The causal matter-frame universe is curvature-regular at the temporal conformal boundary. The apparent Big Bang is a temporal horizon, not a physical curvature singularity. All background and thermal observational pillars are preserved in the screened-limit reduction; the scalar perturbation shape is reproduced, and the tensor-to-scalar ratio is computed from the native temporal-conformal wave equation, yielding values well below observational bounds. Keywords: temporal equivalence principle, temporal horizon cosmology, big bang singularity, static conformal geometry, cosmology, modified gravity, temporal shear Website: https: //mlsmawfield. com/tep/thRepository: https: //github. com/matthewsmawfield/TEP-TH DOI: 10. 5281/zenodo. 20723060 Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All analysis code, configuration files, and manuscripts are open source. Feedback and contributions to further test these results are welcome.
Matthew Lukin Smawfield (Thu,) studied this question.