Galaxy Recession Speed and Lookback Time

Hubble’s Law gives the recession velocity of a galaxy:

v = H₀ × d

For nearby galaxies (d « Hubble radius), this is a good approximation. For very distant galaxies, the full ΛCDM cosmological model is needed for accuracy.

Lookback time (simplified):

t_lookback ≈ d / c (for nearby galaxies, d « c/H₀)

For distant galaxies, the actual lookback time is shorter than d/c because the universe was expanding faster in the past, so the light had to travel “uphill” against expansion.

The Hubble radius (Hubble sphere):

d_Hubble = c / H₀ ≈ 14.5 Gly (gigalight-years, for H₀ = 67.4 km/s/Mpc)

Galaxies beyond this distance recede faster than the speed of light. This is not a violation of special relativity — it is space itself expanding. Two horizons get mixed up here, so it is worth separating them. The particle horizon, about 46 billion light-years out in comoving distance, is the edge of everything whose light has already had time to reach us. That is the observable universe, and it grows as time passes. The boundary past which light emitted today will never reach us is the cosmic event horizon, much closer at roughly 16 billion light-years comoving. Galaxies between the two are still visible, but the photons they are emitting right now will never arrive.

Why v > c is allowed in cosmology: Special relativity limits motion through space to v < c. But cosmic recession is due to the expansion of space — there is no “motion” through a medium. The recession velocity v = H₀d is a coordinate velocity, not a proper velocity through spacetime.

Key distances:

• Andromeda (M31): 2.537 Mly: blueshifted, approaching!
• Virgo Cluster: 53.8 Mly (megalight-years): recession v ≈ 1,155 km/s at H₀ = 70
• Coma Cluster: 320 Mly: v ≈ 6,868 km/s at H₀ = 70
• Most distant galaxy confirmed so far: JADES-GS-z14-0 at z ≈ 14.3, roughly 33 Gly comoving. We see it as it was about 290 million years after the Big Bang