Cosmology

Cosmological distances

Choose one known value: redshift z or present-day comoving distance D_C. Calculate to obtain the other distances and the time since emission. The example menu changes z; it does not calculate automatically.

What the results mean

D_C describes the present-day separation along the line of sight in the expanding model. D_L converts bolometric luminosity to observed flux. D_A converts an angular size to the physical transverse size at emission; the angular scale is kpc per arcsecond. These are different distance definitions, not alternative measurements of the same ruler length. Lookback time is time since emission; age is the universe’s age at emission. Gyr means a billion years, Myr a million. The distance modulus is undefined at z = 0 and shown as a dash. Photometry may additionally require extinction and a K-correction.

Model and limits

Spatially flat ΛCDM, H₀ from 40 to 100 km/s/Mpc, Ωₘ from 0.001 to 0.99991, and z from 0 to 1100. Radiation is fixed at Ω_r = 0.00009; Ω_Λ = 1 − Ωₘ − Ω_r. E(z)² = Ω_r(1+z)⁴ + Ωₘ(1+z)³ + Ω_Λ. D_C = (c/H₀) ∫ dz/E(z), D_L = (1+z)D_C, D_A = D_C/(1+z). Times follow the same expansion model. Distances are integrated in log(1+z); the monotone D_C relation is inverted only within the stated range.

The defaults are illustrative Planck-like values, not a complete Planck fit. This simplified constant-radiation model has no massive-neutrino evolution, spatial curvature, peculiar velocity, or changing dark energy. Radiation does not adjust with H₀. It does not convert cosmological redshift into a special-relativistic Doppler velocity, or infer recombination history from z = 1100.

Hogg: Distance measures in cosmology · Wright: cosmology calculator