Kosmologie

Flat ΛCDM cosmology. Defaults are Planck 2018: H₀ = 67.4 km/s/Mpc, Ω_m = 0.315, Ω_Λ = 0.685. Provide exactly one of {z, v, D_C} — the rest are computed against the same cosmology.

Distances

• Hubble distance: c / H₀
• Comoving distance: D_C = (c/H₀) ∫₀ᶻ dz' / E(z'), with E(z) = √(Ω_m(1+z)³ + Ω_Λ) (Simpson, 1024 intervals)
• Luminosity distance: D_L = (1+z) D_C
• Angular diameter distance: D_A = D_C / (1+z)
• Lookback time: t_L = (1/H₀) ∫₀ᶻ dz' / [(1+z') E(z')]

Velocity ↔ redshift

Hubble's law (linear): v = c·z (small z only). Special relativity: 1+z = √((1+β)/(1−β)), β = v/c. The two diverge for z > 0.1; the cosmology gives the only physically meaningful "distance" at high z.