At Redshift z
Instructions
- Adjust H₀ to see slope change
- Change Ω_m for curvature effects
- Enter redshift for distances
- Observe distance-redshift relations
Plot supernovae on a Hubble diagram—fit cosmological parameters from luminosity distance vs redshift
In an expanding universe, "distance" is ambiguous. Different distance measures—comoving, luminosity, angular diameter—answer different physical questions. Standard candles like Type Ia supernovae let us measure these distances and map the expansion history, leading to the discovery of dark energy in 1998.
The distance between two points in a coordinate system that expands with the universe. It remains constant as space expands. Computed as D_c = c ∫₀z dz'/H(z').
Inferred from apparent brightness: L/(4πD_L²) = observed flux. For flat universe, D_L = (1+z)D_c. The (1+z) factor accounts for both photon dilution and redshift energy loss.
Inferred from angular size: D_A = physical_size / angular_size. Related by D_A = D_c/(1+z). Counterintuitively, D_A decreases at high z in dark energy models.
The Hubble diagram plots distance vs. redshift. For small z, it's linear: D ≈ cz/H₀ (Hubble's law). At high z, curvature depends on Ωm and ΩΛ. Type Ia supernovae trace this curve precisely, revealing accelerated expansion.