IndisputableMonolith.Cosmology.CMBAcousticPeakRatios
The module establishes acoustic peak ratios in the CMB as exact instances of the golden ratio φ from the Recognition Science φ-ladder. Cosmologists testing the BIT-derived power spectrum against observations would cite these ratios. Each ratio follows as a direct specialization of the adjacent wavenumber ratio proved in the upstream structure formation module.
claimThe second-to-first acoustic peak ratio equals $\phi$.
background
The module sits in the cosmology domain and imports the RS time quantum $\tau_0 = 1$ tick. It rests on StructureFormationFromBIT, whose doc-comment states: "The matter power spectrum P(k) of cosmological structure formation inherits the φ-ladder structure of the BIT kernel: at the canonical substrate the ratio between adjacent peak wavenumbers is φ."
The module applies this general wavenumber ratio to the specific acoustic peaks of the cosmic microwave background.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the explicit φ ratios that link the BIT kernel to observable CMB features. It feeds downstream comparisons with Planck data through sibling results such as planck_ratio_2_1. It realizes the T6 self-similar fixed point and the φ-ladder prediction for acoustic peaks within the Recognition Science chain.
scope and limits
- Does not derive absolute multipole locations of the peaks.
- Does not incorporate baryon acoustic oscillation shifts.
- Does not model the damping tail or polarization spectra.
depends on (2)
declarations in this module (15)
-
theorem
ratio_2_1 -
theorem
ratio_3_2 -
theorem
ratio_3_1 -
theorem
ratio_2_1_band -
theorem
phi_sq_band -
theorem
ratio_3_1_band -
def
planck_l_1 -
def
planck_l_2 -
def
planck_l_3 -
def
planck_ratio_2_1 -
theorem
planck_ratio_2_1_value -
theorem
planck_ratio_not_directly_phi -
structure
CMBAcousticPeakRatiosCert -
def
cmbAcousticPeakRatiosCert -
theorem
cmb_acoustic_peak_ratios_one_statement