Universe Simulator — Life (Carbon & Alternatives) + α×G Heatmap + Friedmann

1) Fundamental constants (fine-tuning)

α (fine-structure) μ = mₑ/mₚ Δ(mₙ−mₚ) [MeV] Strong force (x) Gravity G (x)

Chance (noise) % Directionality (“God”) % Sensitivity (0–1)

These windows are plausible heuristics for teaching. They do not replace ab-initio quantum chemistry.

2) Minimal cosmology + Friedmann

Ωm (matter) Ωr (radiation) ΩΛ (dark energy) H₀ (km/s/Mpc)

Available time (Gyr)

Ωk (curvature)

—

Cosmology checks

—

t(rad=mat)

—

t(Λ dominates)

—

Structure window

—

RK4 integration of Friedmann: \( \dot a = a H(a) \), with \( H(a)=H_0\sqrt{\Omega_r a^{-4}+\Omega_m a^{-3}+\Omega_k a^{-2}+\Omega_\Lambda} \).

3) Planetary environment

Surface temperature (K) Surface pressure (bar) Main solvent UV/X environment (x)

Approximate liquid windows (1 bar, reference):

Water

273–373 K

Ammonia

195–240 K

Methane

90–112 K

Ethane

90–185 K

CO₂ (supercritical)

T≥304 K & P≥73 bar

Ranges shift with pressure; high UV breaks fragile molecules (penalized).

4) Result & Diagnostics

Carbon-based: — Alternative life: —

Components (0–100)

Subscores: Chemistry/Atoms, Stars (G), Cosmology (with Friedmann), Solvent/UV.

5) Essential molecules

Qualitative assessments via heuristics (bonding/element production and environment). Educational.

6) Detailed cosmology — a(t)

a(t) normalized so that a(tf)=1; markers for radiation–matter equality and matter–Λ when they occur.

7) α×G heatmap — Habitability zones

α=— • G=— • score=—

X-axis: α (0.005 → 0.010). Y-axis: G (0.3 → 2.0). Green = better, red = worse.