EBC at the Boltzmann Level: Native Confirmation of the Trilemma and an Elastic Shear-Channel Quadrupole

Abstract

Elastic Bounce Cosmology (EBC) predicts a present-day equation of state w₀ = −2/3 without free parameters, and the foundation paper [1] identified two standing tensions with data while treating the model at the background and linear-analytic level. We implement EBC natively in the CLASS Boltzmann code and re-examine both tensions. Neither is relieved. First, re-inferring the physical matter density within EBC rather than adopting a ΛCDM value, we confirm the trilemma between the CMB-preferred ωₘ, the BAO-preferred Ωₘ and the w₀-forced low H₀ at ≈ 6–7σ; the EBC background partially relieves the tension of its own accord, so that the 10.6σ quoted in [1, §9.5] is superseded, but the remainder is not reachable by any parameter left free. Second, and available only at the Boltzmann level, the elastic shear channel of the material medium sources anisotropic stress that raises the CMB temperature quadrupole by a factor of 4.6, and by 3.4 even at the minimum rigidity a stable theory permits. Since the observed quadrupole is low, the prediction is anti-aligned with the data, and the rigidity sector — previously constrained only by stability — is bounded by the low-ℓ CMB with no admissible window remaining. Relaxing the medium's reference state damps the effect without removing it. Both results are consequences of the structurally fixed w₀ = −2/3. We report them as sharpening rather than softening the case against EBC in its present form. Patch scripts, gate suites and build documentation are deposited with this paper. [1] W. Mattis, Elastic Bounce Cosmology (v6), https://doi.org/10.5281/zenodo.21245549