Standard cosmology explains the Cosmic Microwave Background (CMB) acoustic peaks, the pre-recombination sound horizon, and the thermal scaling relevant to Big Bang Nucleosynthesis (BBN) within an FLRW expansion history conventionally extrapolated toward a Big Bang singularity. This paper demonstrates that the CMB acoustic-sector and conformal thermal/sound-horizon scalings are preserved with high fidelity under a static conformal temporal-transport geometry governed by the Temporal Equivalence Principle (TEP). In the TEP framework, matter clocks and photon phases evolve in a causal matter metric defined by a conformal scalar field gₜilde₌ₔ ₍ₔ = A (phi) ² g₌ₔ ₍ₔ. Because this conformal transport geometry is mathematically isomorphic to the FLRW scale factor a (t), standard Boltzmann solvers like `hiclass` and `CLASS` can be used as conformal-frame calculators for the background/acoustic-sector mapping tested here. The parameter traditionally identified as Dark Energy (OmegaLambda) is operationally reinterpreted within this implementation as the homogeneous temporal-shear background contribution filling the same background budget slot, Omegaₚhi. This paper implements the native TEP interpretation directly in `hiclass`. Within the broader TEP interpretation, by recognizing that the spatial metric does not stretch, the "Big Bang" is reinterpreted not as a physical density singularity, but as an observational Temporal Horizon—an asymptotic boundary where the conformal clock-rate field A (phi) -> 0. Direct Boltzmann integration verifies this background/acoustic mathematical isomorphism, confirming that the static conformal geometry preserves the pre-recombination sound horizon to parts-per-million and leaves the acoustic-peak morphology intact without invoking early-universe spatial expansion. Beyond the background mapping, the paper closes the linear pure-conformal scalar perturbation sector by deriving the runtime Bellini–Sawicki functions alphaM = -2 alphaA, alphaB = 2 alphaA, alphaK = -5 alphaA², and alphaT = 0, for which the physical no-ghost discriminant satisfies D = alphaK + (3/2) alphaB² = alphaA². An active-perturbation hiclass run evolving delta phi through the full Einstein–Boltzmann hierarchy produces posteriors statistically indistinguishable from the background-only chain, demonstrating that the implemented linear pure-conformal scalar perturbation sector is stable and observationally negligible at the current homogeneous-amplitude bound. A joint `hiclass` Cobaya MCMC (Planck 2018 low-l TT/EE + lensing + BAO + Pantheon+) tests the screened TEP conformal background within the native hiclass implementation, while companion TEP-C0 (Paper 26) nested sampling over Pantheon+ provides robust quantitative evidence that the screened TEP conformal geometry matches the Pantheon+ distance-redshift relation with Bayesian evidence statistically indistinguishable from CPL (BF ~32--36 depending on the fixed or free-zT branch), without treating late-time acceleration as primitive spatial acceleration. Within the TEP framework, the Hubble tension is interpreted as a late-time, environment-dependent clock-transport effect (Paper 11) caused by the mass-screening of the scalar field, rather than through a crisis in early-universe physics. Keywords: cosmology theory, cosmic microwave background, static conformal geometry, scalar-tensor theories, conformal gravity, 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.
Matthew Lukin Smawfield (Mon,) studied this question.