Temporal Equivalence Principle: Temporal Horizon Cosmology and the Absence of a Physical Big Bang Singularity

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 a_eff 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 a_eff->0 limit is not a physical curvature singularity but a temporal horizon. Two distinct projections of the temporal field are required: A_clock(z)=(1+z)^(-1) is the exact observational clock/redshift mapping that drives a_eff->0 as z->infinity, while A_dyn(z)=(1+z/z_t)^(-epsilon_eff(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 A_clock(eta)=C eta^(-p) with 0 < p <= 1/2, all polynomial curvature invariants vanish at the boundary, timelike proper time diverges, and null geodesics have divergent affine parameter. The singular lower edge of standard flat Lambda CDM is replaced by a smooth temporal conformal boundary T^-, where A_clock->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 T_lock=0.03 eV with transition redshift z_t=100 and T_0=2.725 K, giving strong epoch-by-epoch screening (S_epoch~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 A_clock, yielding a power spectrum P_zeta(k) proportional to k^(n_s-1) with spectral-flow parameter n_s-1=-2 epsilon_field. The observed Planck value n_s=0.965 constrains epsilon_field=0.0175. Tensor modes are derived directly from the temporal-conformal metric: for A_clock(eta)~eta^(-p) the tensor source term A_clock''/A_clock=p(p+1)/eta^2->0 at the horizon, so the tensor equation approaches the Minkowski vacuum. The imported inflationary consistency relation r=16 epsilon_field is not assumed. Numerical integration of the native tensor equation across the finite transition profile yields r(k_pivot)=9x10^-6 and r_max=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.