Scale factor

This article deals with a cosmological parameter; see also scale factor (audio coding) in audio data compression and scale factor in geodesy and cartography.

The scale factor is a cosmological parameter of the Friedmann-Lemaître-Robertson-Walker model . It is a function of time and indicates the relative expansion of the universe , that is, it establishes a connection between physical coordinates and coordinates that move along with it : ${\displaystyle a}$  ${\displaystyle L}$ ${\displaystyle \lambda }$

${\displaystyle a(t)={\frac {L}{\lambda }}.}$

The scale factor can in principle have the unit of a length or be dimensionless . In modern cosmology it is usually chosen without dimensions, so that:

${\displaystyle a(t_{0})=1.}$

The time t is measured from the creation of the universe and represents the current age of the universe with (13.7 ± 0.2) billion years. ${\displaystyle t_{0}}$

The development of the scale factor over time is determined by the formulas of the general theory of relativity , which in the case of a locally isotropic and locally homogeneous universe are represented by the Friedmann equations .

The scale factor and its change over time define the Hubble parameter :

${\displaystyle H={\frac {{\dot {a}}(t)}{a(t)}}.}$

literature

• Arnold Hanslmeier : Introduction to Astronomy and Astrophysics , Spectrum Akademischer Verlag, 2nd edition 2007, ISBN 978-3-8274-1846-3