Difference between revisions of "Hubble's Law and Scale Factors"

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===Reference Material===
 
===Reference Material===
 
* [https://en.wikipedia.org/wiki/Hubble%27s_law Hubble's Law (Wikipedia)]
 
* [https://en.wikipedia.org/wiki/Hubble%27s_law Hubble's Law (Wikipedia)]
 +
* [https://en.wikipedia.org/wiki/Scale_factor_(cosmology) The Scale Factor (Wikipedia)]
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* [http://timtrott.co.uk/scale-factor/ Cosmic Scale Factor (Tim Trott)]
  
 
<latex>
 
<latex>
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the expansion of the universe is  
 
the expansion of the universe is  
 
$H_0^{-1}\approx{h\over 10^{11}}yrs\approx 9.778h^{-1}Gyrs$.
 
$H_0^{-1}\approx{h\over 10^{11}}yrs\approx 9.778h^{-1}Gyrs$.
 +
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\section*{ The Scale Factor, $a(t)$ }
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$a(t)$ relates physical ($r$) and {\it comoving} ($x$) coordinates in an
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expanding universe:
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$$\begin{align}
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r&=a(t)x\\
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\dot r&=\dot ax+a\dot x=\underbrace{\aa}_{\equiv H}r+\underbrace{a\dot x}_{\equiv v_p}\\
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\end{align}$$
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Thus, the two components of physical velocity are $H$ (the Hubble expansion
 +
parameter) and $v_p$ (the peculiar velocity, or motion relative to expansion)
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By convention, $t_0 \equiv$ today and $a(t_0)=1$.
  
  
 
\end{document}
 
\end{document}
 
</latex>
 
</latex>

Revision as of 13:42, 17 January 2017

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Reference Material

Hubble’s Law (1929)

Hubble’s Law is an empirical law stating that, on large scales, recessional velocity is proportional to distance from observer.

where , the Hubble parameter, is not constant, but can vary slowly with time. By convention, is often expressed as , where 1 parsec (pc) , is the distance at which 1 AU appears as 1 arcsec on the sky. The Hubble Space Telescope Key Project (Freedman et al. ApJ 553, 47, 2001) measured the present day value of Hubble Constant , giving us that the current timescale for the expansion of the universe is .

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 .