% miko:type: atomic
% miko:title: Hubble Law
% miko:summary: The low-redshift relation between recession speed and distance.
% miko:tags: cosmology
% miko:difficulty: undergrad
% miko:related: complete-cosmology, scale-factor-redshift, friedmann-equations
% miko:keywords: Hubble parameter, expansion, distance

\documentclass{article}
\usepackage{amsmath}
\title{Hubble Law}
\begin{document}
\maketitle

\section{Local Law}

For sufficiently nearby galaxies,

$$
v \simeq H_0 d.
$$

This is the first-order expansion law around the present epoch. $H_0$ is the
current value of the Hubble parameter.

\section{From Scale Factor}

For proper distance $D=a(t)\chi$ at fixed comoving coordinate $\chi$,

$$
\dot D = \dot a\chi = \frac{\dot a}{a}D = HD.
$$

Thus Hubble's law is the local form of metric expansion.

\end{document}
