% miko:type: atomic
% miko:title: Cosmological Constant
% miko:summary: The constant energy density term associated with accelerated expansion.
% miko:tags: cosmology
% miko:difficulty: undergrad
% miko:related: complete-cosmology, friedmann-equations, critical-density
% miko:keywords: Lambda, dark energy, acceleration

\documentclass{article}
\usepackage{amsmath}
\title{Cosmological Constant}
\begin{document}
\maketitle

\section{In Einstein's Equation}

The cosmological constant appears as

$$
G_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}.
$$

It can be moved to the matter side and interpreted as a constant vacuum energy
density.

\section{Equation of State}

Vacuum energy has

$$
p_\Lambda = -\rho_\Lambda c^2.
$$

The negative pressure makes it contribute positively to $\ddot a$ in the
Friedmann acceleration equation.

\end{document}
