% miko:type: atomic
% miko:title: Cosmic Microwave Background
% miko:summary: Relic blackbody radiation from the epoch when photons decoupled from matter.
% miko:tags: cosmology
% miko:difficulty: undergrad
% miko:related: complete-cosmology, scale-factor-redshift, friedmann-equations
% miko:keywords: CMB, recombination, blackbody

\documentclass{article}
\usepackage{amsmath}
\title{Cosmic Microwave Background}
\begin{document}
\maketitle

\section{Origin}

The early universe was hot and ionized, so photons scattered frequently from
free electrons. When the universe cooled enough for neutral atoms to form,
photons decoupled and began to travel freely.

\section{Temperature Scaling}

Radiation temperature scales as

$$
T \propto \frac{1}{a}.
$$

The observed microwave background is the redshifted remnant of this early hot
radiation field.

\section{Why It Matters}

The CMB is evidence for a hot early universe. Its anisotropies encode the
initial conditions for structure formation.

\end{document}
