>[!warning] >This content has not been peer reviewed. # Milgrom MOND (RST) — Code Script: `rst_milgrom_mond.py`. ## Purpose Generates a **single 2×2 figure** that shows the relevancy of RST for the MOND programme at a glance: 1. **a₀(z)** — RST derives the acceleration threshold from cosmology: a₀(z) = c H(z)/(2π). Not a universal constant; evolves with redshift (flat ΛCDM). 2. **μ(η)** — The interpolation function as geometric projection (L_n-norm); n ≈ 1.24 (derived); SPARC confirms. 3. **Rotation curve** — Hernquist baryons + RST field equation μ(q'/a₀, n) q' = g_N. Core in the center (η ≫ 1 ⇒ μ → 1), MOND-like boost in the outskirts. 4. **v_flat(z)/v_flat(0)** — Deep-MOND scaling (a₀(z)/a₀(0))^(1/4). At z = 2, a₀ is ~3× higher ⇒ flat rotation velocity ~32% higher (JWST-era falsifiable signature). ## Engine Uses **`rst_engine`** at workspace root (three levels up from this folder): - `solve_omega(I, N, n)` — I = g_N, N = a₀, returns Ω = q' (same equation as SPARC and Tremaine Core–Cusp). - `mu_rst(eta, n)` — fidelity μ(η). - `DEFAULT_N` — n ≈ 1.24 (derived); SPARC confirms. ## Parameters (in script) - **Cosmology:** H₀ from 70 km/s/Mpc; flat ΛCDM with Ωm = 0.3, ΩΛ = 0.7. - **Hernquist (rotation curve):** M = 10¹¹ M☉, a = 3 kpc. - **RST:** a₀(z=0) = 1.042×10⁻¹⁰ m/s²; n ≈ 1.24 (derived); SPARC confirms. ## Output - **`milgrom_mond.png`** — 2×2 panels (a₀(z), μ(η), rotation curve, v_flat ratio vs z). Saved in this folder. - Console: short summary (a₀ ratio at z=2, n, v_flat % increase at z=2). ## Run (from workspace root) ``` python "expanded theory applied/further applications/Milgrom MOND/rst_milgrom_mond.py" ``` The script is discovered by **`run_all_further_scripts.py`** and included in the combined further-applications output. --- ## Links - **Application:** [[Milgrom MOND (RST)]] - **Results (figure):** [[Milgrom MOND Results]] - **Same equation (SPARC, Tremaine):** [[expanded theory/sparc evaluation/SPARC evaluation - Code]], [[Tremaine Core-Cusp/Tremaine Core-Cusp - Code]]