Scale Factor and Redshift

Redshift

Observed redshift is defined by

$$1+z=\frac{\lambda_{\rm obs}}{\lambda_{\rm em}}.$$

In an expanding FLRW universe, photon wavelengths scale with $a(t)$, so

$$1+z = \frac{a_0}{a_{\rm em}}.$$

Interpretation

Large redshift means the light was emitted when the universe was smaller. This does not mean the photon moved through ordinary static space and lost energy by friction. It reflects the changing spacetime geometry.