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The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922〔 (English translation: ). The original Russian manuscript of this paper is preserved in the (Ehrenfest archive ).〕 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given mass density and pressure . The equations for negative spatial curvature were given by Friedmann in 1924.〔 (English translation: )〕 == Assumptions == (詳細はcosmological principle; empirically, this is justified on scales larger than ~100 Mpc. The cosmological principle implies that the metric of the universe must be of the form : where is a three-dimensional metric that must be one of (a) flat space, (b) a sphere of constant positive curvature or (c) a hyperbolic space with constant negative curvature. The parameter discussed below takes the value 0, 1, −1 in these three cases respectively. It is this fact that allows us to sensibly speak of a "scale factor", . Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. From FLRW metric we compute Christoffel symbols, then the Ricci tensor. With the stress–energy tensor for a perfect fluid, we substitute them into Einstein's field equations and the resulting equations are described below. 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「Friedmann equations」の詳細全文を読む スポンサード リンク
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