>[!warning] >This content has not been peer reviewed. # Cosmology and GR — RST foundation **Cosmology** and **GR** (expansion $\theta = 3H$, FLRW; noise floor $a_0 = cH/(2\pi)$; dark energy as baseline) are the eighth foundational area. They supply the physical noise floor and the three regimes (Newton / MOND / $\Lambda$). --- ## I. Classical side - **FLRW:** Homogeneous, isotropic expansion; $\theta = \nabla_\mu u^\mu = 3\dot{a}/a = 3H$. - **Dark energy / $\Lambda$:** Constant energy density; $W \to N$ when $I \to 0$. - **Gravity:** Newton, MOND, and the transition scale $a_0$. --- ## II. Mapping to RRT / RST | Concept | RRT / RST identity | Equation / link | |:---|:---|:---| | **Expansion $\theta$** | $3H$ in FLRW; sets the cosmic "noise" scale. | A4, A5; Noise Floor. | | **Noise floor $a_0$** | $a_0 = c\theta/(6\pi) = cH/(2\pi)$; gravitational threshold. | Noise Floor; RST Core Reduction. | | **Newton regime** | $\Omega \gg N$; $\mu \to 1$; $\Omega = I$. | High SNR. | | **MOND regime** | $\Omega \ll N$; $\mu \to \eta$; $\Omega = \sqrt{I \cdot N}$. | Low SNR. | | **Dark energy** | $I \to 0$; $W \to N$; baseline workload. | RST Part II; $\Lambda$. | So: **cosmology** gives $\theta$, $H$, $a_0$; **GR** gives the geometric setting; together they fix the noise $N$ and the three regimes of the Resource Allocation Equation. At macroscopic scale ($N \to \infty$), accumulated lacunarity yields $D_f \approx 1.86$ and the MOND fidelity $n \approx 1.24$. See [[N to Infinity — Cosmology (RST)]]. --- ## Links - **Graph Size Hierarchy ($N \to \infty$):** [[N to Infinity — Cosmology (RST)]] - **Foundation index:** [[../Foundation index]] - **Noise Floor:** [[expanded theory/Noise Floor]] - **RST Core Reduction:** [[expanded theory/RST Core Reduction]] - **Applications Roadmap:** [[../../Applications Roadmap]]