>[!warning] >This content has not been peer reviewed. # Milgrom MOND (RST) — Results Output from **[[Milgrom MOND - Code]]** (script: `rst_milgrom_mond.py`).  ## What the figure shows 2×2 panels (one-glance relevancy): - **Top-left — a₀(z):** RST identifies the acceleration threshold with the cosmological scale: a₀(z) = c H(z)/(2π). Not a universal constant; at z = 2, a₀ is ~3× the local value. Orange vertical line marks z = 2 (JWST regime). - **Top-right — μ(η):** Interpolation function (geometric projection, L_n-norm); n = 1.25 from SPARC. Green/orange bands: Newton (μ → 1) and deep-MOND (μ → 0) regimes. - **Bottom-left — Rotation curve:** Hernquist baryons + RST (μ(q'/a₀, n) q' = g_N). Core in the center (no extra gravity); MOND-like boost in the outskirts. Same equation as Tremaine Core–Cusp and SPARC. - **Bottom-right — v_flat(z)/v_flat(0):** Deep-MOND scaling (a₀(z)/a₀(0))^(1/4). At z = 2, flat rotation velocity is ~31% higher for fixed baryonic mass (JWST-era falsifiable signature). --- ## Gate 1: RST vs LCDM vs static-MOND at z = 2 **This is RST's strongest falsifiable prediction.** The v_flat ratio is H0-independent; uncertainty comes from $\Omega_M$ only. | Framework | $v_\text{flat}(z\!=\!2) / v_\text{flat}(0)$ | Difference | |:---|:---|:---| | **RST** ($\Omega_M = 0.30 \pm 0.02$) | **1.312 [1.302, 1.322]** | **+31.2% [+30.2%, +32.2%]** | | LCDM (NFW halos) | ~1.0 $\pm$ 0.1 (model-dependent) | ~0% (halo-dependent) | | Static MOND ($a_0$ = const) | 1.000 | 0% | **Assumptions:** flat $\Lambda$CDM background; deep-MOND limit $v_\text{flat}^4 \sim G M_\text{bar} a_0$; $n \approx 1.24$ (derived; SPARC $1.25 \pm 0.05$ confirms). **Key:** RST predicts $a_0(z) = c H(z) / (2\pi)$. Since $H(z=2)/H(0) \approx 2.97$, the flat velocity at $z = 2$ is $(2.97)^{1/4} \approx 1.31$ times higher than at $z = 0$ for fixed baryonic mass. Static MOND predicts no change. LCDM predicts approximately no change (NFW halo concentration decreases with $z$, but the effect is model-dependent and small). **Falsification:** If JWST/ALMA rotation curves at $z \sim 2$ show $v_\text{flat}$ consistent with $z = 0$ at the same $M_\text{bar}$ (no ~31% boost), RST's evolving $a_0$ is ruled out. ![[gate1_comparison.png]] *Left: v_flat ratio vs redshift (blue band = Omega_M uncertainty). Right: a0 evolution.* --- ## Links - **Application:** [[Milgrom MOND (RST)]] - **Code:** [[Milgrom MOND - Code]]