cosmological redshift

Light from a distant galaxy arrives looking redder than it left: lines that a lab would place in the blue are shifted toward the red end of the spectrum. It is tempting to read this as a Doppler shift, the galaxy speeding away, but the deeper truth is stranger and simpler. While the light was in transit for billions of years, the space it travelled through expanded, and the light wave was stretched along with it. The redness is a measure of how much the universe has grown since the light set out.

The redshift z is defined by z = (lambda_observed - lambda_emitted) / lambda_emitted, so that a line stretched to twice its rest wavelength has z = 1. Its exact meaning in an expanding universe is 1 + z = a(t_observed) / a(t_emitted), the ratio of the scale factor now to the scale factor when the light was emitted. Thus z is not really a velocity at all; it directly reads off how much space has stretched. Light seen at z = 1 left when the universe was half its present size; the cosmic microwave background at z about 1100 left when the universe was roughly a thousand times smaller and correspondingly hotter.

The common misconception is to compute a recession speed from z with the special-relativistic Doppler formula and treat it as motion through space. For nearby galaxies this is a fine approximation, but at large z it is simply wrong, because the effect is the cumulative stretching of space, not a single relative velocity. Cosmological redshift is distinct from the gravitational redshift caused by climbing out of a gravity well, though both make light redder.