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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Scale factor (cosmology) ： ウィキペディア英語版 Scale factor (cosmology) The scale factor, cosmic scale factor or sometimes the Robertson-Walker scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It relates the proper distance (which can change over time, unlike the comoving distance which is constant) between a pair of objects, e.g. two galaxy clusters, moving with the Hubble flow in an expanding or contracting FLRW universe at any arbitrary time $t$ to their distance at some reference time $t\_0$. The formula for this is: :$d(t)\; =\; a(t)d\_0,\backslash ,$ where $d(t)$ is the proper distance at epoch $t$, $d\_0$ is the distance at the reference time $t\_0$ and $a(t)$ is the scale factor. Thus, by definition, $a(t\_0)\; =\; 1$. The scale factor is dimensionless, with $t$ counted from the birth of the universe and $t\_0$ set to the present age of the universe: $13.799\backslash pm0.021\backslash ,\backslash mathrm$〔 〕 giving the current value of $a$ as $a(t\_0)$ or $1$. The evolution of the scale factor is a dynamical question, determined by the equations of general relativity, which are presented in the case of a locally isotropic, locally homogeneous universe by the Friedmann equations. The Hubble parameter is defined: :$H\; \backslash equiv$ where the dot represents a time derivative. From the previous equation $d(t)\; =\; d\_0\; a(t)$ one can see that $\backslash dot(t)\; =\; d\_0\; \backslash dot(t)$, and also that $d\_0\; =\; \backslash frac$, so combining these gives $\backslash dot(t)\; =\; \backslash frac$, and substituting the above definition of the Hubble parameter gives $\backslash dot(t)\; =\; H\; d(t)$ which is just Hubble's law. Current evidence suggests that the expansion rate of the universe is accelerating, which means that the second derivative of the scale factor $\backslash ddot(t)$ is positive, or equivalently that the first derivative $\backslash dot(t)$ is increasing over time. This also implies that any given galaxy recedes from us with increasing speed over time, i.e. for that galaxy $\backslash dot(t)$ is increasing with time. In contrast, the Hubble parameter seems to be ''decreasing'' with time, meaning that if we were to look at some ''fixed'' distance d and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones.〔(Is the universe expanding faster than the speed of light? ) (see final paragraph)〕 According to the Friedmann–Lemaître–Robertson–Walker metric which is used to model the expanding universe, if at the present time we receive light from a distant object with a redshift of ''z'', then the scale factor at the time the object originally emitted that light is $a(t)\; =\; \backslash frac$.〔Davies, Paul (1992), ''The New Physics'', (p. 187 ).〕〔Mukhanov, V. F. (2005), ''Physical Foundations of Cosmology'', (p. 58 ).〕 ==See also== *Cosmological principle *Lambda-CDM model *Redshift 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Scale factor (cosmology)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.