CMB Pipeline

Module Thesis

The CMB power spectrum is derived from ι_τ alone; tensor-to-scalar ratio pre-registered for CMB-S4.

Overview

The cosmic microwave background (CMB) is the oldest observable light in the universe and the most precise dataset in cosmology. The standard $\Lambda$CDM model fits the CMB power spectrum using six free parameters. Category $\tau$ derives the entire CMB pipeline from a single constant – ${\iota }_{\tau }=\frac{2}{\pi +e}$ – with zero adjustable parameters. The decisive near-term test: the tensor-to-scalar ratio $r$, pre-registered for CMB-S4.

The Core Idea

Three headline predictions define the CMB pipeline:

1. Tensor-to-scalar ratio (V.P136): $r={\iota }_{\tau }^4\approx 0.0136$. This is the ratio of gravitational wave perturbations to density perturbations in the primordial spectrum. CMB-S4 will measure $r$ with sufficient precision to confirm or rule out this prediction. If $r$ is inconsistent with ${\iota }_{\tau }^4$, the framework’s cosmological sector falls.

2. Spectral index (V.T197): $n_s=1-\frac{2}{N_e}\approx 0.9649$, where $N_e=57$ e-folds of inflation (derived from ${\iota }_{\tau }$). This matches Planck 2018 observations.

3. First acoustic peak (V.T190): ${\ell }_1=220.6$. The position of the first peak in the CMB angular power spectrum, derived from the sound horizon at recombination.

The framework also derives the Silk damping scale, baryon loading, B-mode polarization amplitude, and BBN light-element abundances – all from ${\iota }_{\tau }$ alone. The Hubble tension (the discrepancy between early- and late-universe measurements of $H_0$) is resolved by the formula $h=\frac{2}{3}+\frac{{\iota }_{\tau }^2}{17}$ at $-120$ ppm.

Why This Matters

The CMB is the framework’s most exposed prediction surface. Every parameter is derived, not fitted. CMB-S4 (expected results ~2028-2030) will either confirm $r={\iota }_{\tau }^4$ or falsify the cosmological sector. This is what the program means by pre-registered falsification.

Key Claims

1. V.P136 – Tensor-to-scalar ratio $r={\iota }_{\tau }^4$, pre-registered for CMB-S4 (tau-effective)
2. V.T190 – First acoustic peak ${\ell }_1=220.6$ (tau-effective)
3. V.T197 – Full CMB pipeline from single constant (tau-effective)
4. Hubble tension resolved: $h=\frac{2}{3}+\frac{{\iota }_{\tau }^2}{17}$ at −120 ppm (tau-effective)