Temporal Equivalence Principle: hiclass Background Implementation and CMB Acoustic Peak Preservation

Standard cosmology relies on spatial expansion and a Big Bang singularity to explain the Cosmic Microwave Background (CMB) acoustic peaks, the pre-recombination sound horizon, and the thermal scaling relevant to Big Bang Nucleosynthesis (BBN). This paper demonstrates that these early-universe successes are natively preserved under a static conformal temporal-transport geometry governed by the Temporal Equivalence Principle (TEP). The TEP addresses late-universe anomalies via a dynamical proper-time field, governed by environment-dependent Gradient Screening with saturation scale rhoT ~ 20 g/cm³ (Paper 0, §7). The scalar field is frozen during radiation domination (Tᵐuₘu ~ 0), and the current numerical analysis isolates the background-only realization as the baseline implementation. This paper implements the native TEP background-only modification directly in hiclass via the transition function fT (z) = ln (1+z) * exp (- (z/zT) ⁿT), with the exact Jordan-frame conformal factor M (z) = A/ (1-alphaA) giving HTEP (z) = HLCDM (z) * M (z) while preserving standard General Relativistic perturbations. The functional form is the shared TEP-C0 implementation (Paper 26): the exp (- (z/zT) ⁿT) factor enforces early-time freezing, so the temporal-shear field is suppressed for z >> zT. Direct Boltzmann integration verifies this phenomenological boundary condition, confirming that the code preserves the pre-recombination sound horizon to parts-per-million (rₛTEP / rₛLCDM = 0. 999994) and leaves the acoustic-peak morphology untouched. The exact geometric relation M = A/ (1-alphaA) is evaluated directly in the production implementation (Section 5. 4 and Appendix A. 3). The only CMB-level effect of a non-zero epsilonT is a late-time angular-diameter-distance projection that rigidly rescales the angular acoustic scale thetaₛ (+0. 185% at the fiducial epsilonT = 0. 0066, zT = 5, nT = 2) and is largely degenerate with H₀. A joint hiclass Cobaya MCMC (Planck 2018 low-l TT/EE + lensing + BAO + Pantheon+) yields epsilonT = 0. 0056 +/- 0. 0043 and H₀ = 66. 63 +/- 1. 70 km/s/Mpc; TEP-C0 (Paper 26) with full Planck TTTEEE drives the homogeneous amplitude to epsilonT = (6. 75 +/- 0. 24) x 10^-6. Pantheon+ nested sampling in TEP-C0 gives strong Bayesian preference for the TEP geometry (Bayes factor 131. 6 vs Lambda CDM for zT = 5). Within the TEP framework, the Hubble tension is interpreted as a late-time, environment-dependent clock-transport effect (Paper 11) rather than through a crisis in early-universe physics. Keywords: cosmology theory, cosmic microwave background, static universe, scalar-tensor theories, conformal gravity, Hubble tension, modified gravity, effective field theory of dark energy, hiclass, Horndeski, temporal equivalence principle, proper time, Cobaya, Planck 2018 Website: https: //mlsmawfield. com/tep/hcRepository: https: //github. com/matthewsmawfield/TEP-HC DOI: 10. 5281/zenodo. 20572722 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.