% miko:type: atomic
% miko:title: Scale Factor and Redshift
% miko:summary: Cosmological redshift is the stretching of photon wavelengths by the expansion of space.
% miko:tags: cosmology
% miko:difficulty: undergrad
% miko:related: complete-cosmology, hubble-law, friedmann-equations
% miko:keywords: scale factor, redshift, wavelength

\documentclass{article}
\usepackage{amsmath}
\title{Scale Factor and Redshift}
\begin{document}
\maketitle

\section{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

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

\section{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.

\end{document}
