Difference between revisions of "Scale Factor"

From AstroBaki
Jump to navigationJump to search
 
Line 1: Line 1:
 
===Short Topical Videos===
 
===Short Topical Videos===
* [https://www.youtube.com/watch?v=73YenHClXTs Cosmic Event Horizon - Scale Factor - Accelerated Expansion (Reed Jeffrey, Upper Canada College)]
+
*  
  
 
===Reference Material===
 
===Reference Material===
 
* [https://en.wikipedia.org/wiki/Scale_factor_(cosmology) The Scale Factor (Wikipedia)]
 
* [https://en.wikipedia.org/wiki/Scale_factor_(cosmology) The Scale Factor (Wikipedia)]
 +
* [http://timtrott.co.uk/scale-factor/ Cosmic Scale Factor (Tim Trott)]
  
 
<latex>
 
<latex>
\documentclass[]{article}
+
\documentstyle[11pt]{article}
\usepackage[top=1in,bottom=1in,left=1in,right=1in]{geometry}
+
 
 +
\def\:{\ddot }
 +
\def\.{\dot }
 +
\def\^{\hat }
 +
\def\_{\bar }
 +
\def\~{\tilde }
 +
\def\hf{\frac12}
 +
\def\imply{\Rightarrow}
 +
\def\inv#1{{1\over #1}}
 +
\def\ddt{{d\over dt}}
 +
\def\aa{{\dot a \over a}}
 +
\def\adda{{\ddot a \over a}}
 +
\def\thnot{\theta_0}
 +
\def\etot{\Omega_0}
 +
\def\econs{\Omega_{0,\Lambda}}
 +
\def\emat{\Omega_{0,M}}
 +
\def\econs{\Omega_{0,\Lambda}}
 +
\def\p{^\prime}
 +
\def\iff{\Leftrightarrow}
 +
\def\xv{{\vec x}}
 +
\def\pv{{\vec p}}
 +
\def\vv{{\vec v}}
 +
\def\ppt{{\partial\over\partial t}}
 +
\def\ddt{\frac{d}{dt}}
 +
\def\epot{{8\pi \over 3}}
 +
 
 +
\usepackage{fullpage}
 
\usepackage{amsmath}
 
\usepackage{amsmath}
\usepackage{graphicx}
 
\usepackage{natbib}
 
 
\usepackage{eufrak}
 
\usepackage{eufrak}
  
 
\begin{document}
 
\begin{document}
\section{The Scale Factor $a(t)$}
+
\section*{ The Scale Factor, $a(t)$ }
 +
 
 +
$a(t)$ relates physical ($r$) and {\it comoving} ($x$) coordinates in an
 +
expanding universe:
 +
$$\begin{align}
 +
r&=a(t)x\\
 +
\dot r&=\dot ax+a\dot x=\underbrace{\aa}_{\equiv H}r+\underbrace{a\dot x}_{\equiv v_p}\\
 +
\end{align}$$
 +
Thus, the two components of physical velocity are $H$ (the Hubble expansion
 +
parameter) and $v_p$ (the peculiar velocity, or motion relative to expansion)
 +
By convention, $t_0 \equiv$ today and $a(t_0)=1$.
  
 
\end{document}
 
\end{document}
<\latex>
+
</latex>

Latest revision as of 23:58, 17 January 2016

Short Topical Videos[edit]

Reference Material[edit]

The Scale Factor,

relates physical () and comoving () coordinates in an expanding universe:

Thus, the two components of physical velocity are (the Hubble expansion parameter) and (the peculiar velocity, or motion relative to expansion) By convention, today and .