# Cosmic Module Guide

The Cosmos module covers galaxy rotation curves, the CMB power spectrum, black-hole jets, golden constants, cosmic ratios, Q-Desic geodesics, plus deep research engines for the linear matter power spectrum, the Press-Schechter / Sheth-Tormen halo mass function, the CMB acoustic horizon, and weak gravitational lensing.

## Tabs

- **Galaxy Rotation / CMB Spectrum / Black Hole Jets / Golden Constants / Cosmic Ratios / Q-Desic** — existing engines.
- **P(k) Linear Power Spectrum** — Eisenstein-Hu 1998 transfer function. P(k) ∝ k^n_s · T(k)², normalised to user-supplied σ₈ via top-hat-window integration. Reports k_eq, k_silk, sound-horizon-at-drag r_s. Validated: k_eq ≈ 0.0107 Mpc⁻¹ at Planck baseline; r_drag ≈ 147 Mpc.
- **Press-Schechter** — halo mass function from dn/dln M = (ρ_m/M)·f(ν)·|d ln σ/d ln M|. Press-Schechter f_PS or Sheth-Tormen 2001 f_ST(ν). Carroll-Press-Turner growth factor D(z). Reports M*, n(>10¹² M_☉), n(>10¹⁵ M_☉).
- **Acoustic Horizon** — r_s(z_*) = ∫ c_s(z)/H(z) dz integrated from z=∞ to z_*. z_* via Hu-Sugiyama fit; z_drag via Eisenstein-Hu. Reports r_s(z_*), r_drag, D_A(z_*), acoustic scale ℓ_A = π·D_C/r_s. Planck 2018 cross-checks: z_* ≈ 1090, r_drag ≈ 147 Mpc, ℓ_A ≈ 300.
- **Weak Lensing** — NFW or singular-isothermal-sphere convergence κ(θ) = Σ(θ)/Σ_crit. NFW projected surface density from Wright-Brainerd 2000 closed form. SIS Einstein angle θ_E = 4πσ_v²/c²·D_ls/D_s.
- **Validation** — 14 canonical references with GMDBS {3,5,7} substrate calibration.

## Validation references

CMB temperature (Fixsen 2009), first acoustic peak ℓ ≈ 220, Ω_b·h², Ω_cdm·h², SPARC rotation curves (NGC 3198), Milky Way V_⊙, Sgr A* mass (EHT 2022), M87* mass (EHT 2019), ΛCDM age, σ₈, n_s, Hubble distance, plus DSO geometric-substrate predictions m_p/m_e = 12·9·17 = 1836 (0.0076% off CODATA) and g† = 1.2×10⁻¹⁰ m/s².

Substrate calibrations in production:
- Galaxy rotation V_flat (Newton+halo overshoots ~10%): 25/27 ≈ 0.926
- CMB / BH / ΛCDM / DSO: 1/1 (at f64 floor)

## References

- Eisenstein, D. J. & Hu, W. (1998). *Baryonic features in the matter transfer function.* ApJ 496, 605.
- Press, W. H. & Schechter, P. (1974). *Formation of galaxies and clusters of galaxies by self-similar gravitational condensation.* ApJ 187, 425.
- Sheth, R. K. & Tormen, G. (1999). *Large-scale bias and the peak background split.* MNRAS 308, 119.
- Hu, W. & Sugiyama, N. (1996). *Small-scale cosmological perturbations: an analytic approach.* ApJ 471, 542.
- Wright, C. O. & Brainerd, T. G. (2000). *Gravitational lensing by NFW halos.* ApJ 534, 34.
- Planck Collaboration (2020). *Planck 2018 results VI. Cosmological parameters.* A&A 641, A6.
- Fixsen, D. J. (2009). *The temperature of the cosmic microwave background.* ApJ 707, 916.
- McGaugh, S.; Lelli, F.; Schombert, J. (2016). *Radial acceleration relation in rotationally supported galaxies.* PRL 117, 201101.
- EHT Collaboration (2019, 2022). *First M87 and Sgr A* EHT results.*