What question did this study set out to answer?

The study investigates the cosmic microwave background (CMB) power spectrum using the Interior Observer framework of black hole cosmology.

March 8, 2026Open Access

The Full CMB Power Spectrum in Black Hole Cosmology: A CLASS Boltzmann Code Analysis (Interior Observer Paper 6)

Key Points

The study investigates the cosmic microwave background (CMB) power spectrum using the Interior Observer framework of black hole cosmology.
Utilized the CLASS Boltzmann code to compute the full CMB TT angular power spectrum.
Conducted a parameter sensitivity scan on matter density (Ω_m) and curvature density (Ω_k).
Validated CMB parameters against ΛCDM and Planck observations.
Analyzed first peak heights and positions in context of early matter-radiation equality.
Identified the first peak as 33% taller than ΛCDM predictions due to enhanced integrated Sachs-Wolfe effect.
Observed a uniform shift of all five acoustic peaks to larger angular scales by ~17%.
Found that no combination of IO parameters can reproduce the standard ℓ₁ = 220 without violating bounds or requiring extreme H₀ values.
Demonstrated that the sound horizon at baryon drag is larger by 23% compared to ΛCDM.

Abstract

Paper 6 in the Interior Observer (IO) cosmological framework, which proposes the observable universe exists inside a Schwarzschild black hole. The full CMB TT angular power spectrum is computed using the CLASS Boltzmann code (v3. 3. 4) with IO framework parameters (H₀ = 58. 2 km/s/Mpc, Ωₘ = 0. 197, Ωₖ = −0. 130, TCMB = 2. 6635 K) and ΛCDM primordial parameters (Aₛ, nₛ, τᵣeio). ΛCDM validation passes: ℓ₁ = 221, matching Planck. The IO spectrum is a clean geometric rescaling of ΛCDM — all five acoustic peaks are shifted uniformly ~17% to larger angular scales (ℓ₁ = 180, ℓ₂ = 445, ℓ₃ = 690, ℓ₄ = 950, ℓ₅ = 1204). Peak spacing, odd-even asymmetry, damping tail, and baryon loading physics are preserved. The first peak is 33% taller due to enhanced early integrated Sachs-Wolfe effect from earlier matter-radiation equality (zₑq = 1748 vs 3403). The IO framework does not break plasma physics — it changes the geometric ruler. A two-dimensional parameter sensitivity scan over Ωₘ ∈ 0. 15, 0. 315 and Ωₖ ∈ −0. 20, −0. 02, with H₀ derived self-consistently from the IO geometric constraint, reveals that ℓ₁ is structurally locked to 171, 198 across the entire viable parameter space. No combination of IO parameters can reproduce ℓ₁ = 220 without requiring H₀ 1100 without altering the late-time BAO fit — notably the same requirement identified by the broader cosmology community for the Hubble tension. All CLASS outputs independently verified by analytical computation (Wolfram/ChatGPT 5. 3). Peak positions are zero-parameter IO predictions; absolute peak heights are not claimed (borrowed Aₛ). Relative peak ratios (including the eISW first-peak enhancement) are emergent physical properties of the IO matter-radiation equality epoch. Multi-AI research: Claude Code (Anthropic) for CLASS computation and parameter scan; Wolfram/ChatGPT 5. 3 (OpenAI + Wolfram) for analytical verification; Gemini 2. 5 Pro (Google DeepMind) for adversarial review; Claude (Anthropic) for orchestration. Companion to Paper 1 (DOI: 10. 5281/zenodo. 18854813), Paper 2 (DOI: 10. 5281/zenodo. 18868612), Paper 3 (DOI: 10. 5281/zenodo. 18876346), Paper 4 (DOI: 10. 5281/zenodo. 18883069), and Paper 5 (DOI: 10. 5281/zenodo. 18889865).

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David Fife (Fri,) studied this question.

synapsesocial.com/papers/69ada90bbc08abd80d5bc608 https://doi.org/https://doi.org/10.5281/zenodo.18891474

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