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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 Flatness problem ： ウィキペディア英語版 Flatness problem The flatness problem (also known as the oldness problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that a small deviation from these values would have had massive effects on the nature of the universe at the current time. In the case of the flatness problem, the parameter which appears fine-tuned is the density of matter and energy in the universe. This value affects the curvature of space-time, with a very specific critical value being required for a flat universe. The current density of the universe is observed to be very close to this critical value. Since the total density departs rapidly from the critical value over cosmic time, the early universe must have had a density even closer to the critical density, departing from it by one part in 1062 or less. This leads cosmologists to question how the initial density came to be so closely fine-tuned to this 'special' value. The problem was first mentioned by Robert Dicke in 1969. The most commonly accepted solution among cosmologists is cosmic inflation, the idea that the universe went through a brief period of extremely rapid expansion in the first fraction of a second after the Big Bang; along with the monopole problem and the horizon problem, the flatness problem is one of the three primary motivations for inflationary theory. ==Energy density and the Friedmann equation== According to Einstein's field equations of general relativity, the structure of spacetime is affected by the presence of matter and energy. On small scales space appears flat – as does the surface of the Earth if one looks at a small area. On large scales however, space is bent by the gravitational effect of matter. Since relativity indicates that matter and energy are equivalent, this effect is also produced by the presence of energy (such as light and other electromagnetic radiation) in addition to matter. The amount of bending (or curvature) of the universe depends on the density of matter/energy present. This relationship can be expressed by the first Friedmann equation. In a universe without a cosmological constant, this is: :$H^2\; =\; \backslash frac\; \backslash rho\; -\; \backslash frac$ Here $H$ is the Hubble parameter, a measure of the rate at which the universe is expanding. $\backslash rho$ is the total density of mass and energy in the universe, $a$ is the scale factor (essentially the 'size' of the universe), and $k$ is the curvature parameter — that is, a measure of how curved spacetime is. A positive, zero or negative value of $k$ corresponds to a respectively closed, flat or open universe. The constants $G$ and $c$ are Newton's gravitational constant and the speed of light, respectively. Cosmologists often simplify this equation by defining a critical density, $\backslash rho\_c$. For a given value of $H$, this is defined as the density required for a flat universe, i.e. . Thus the above equation implies :$\backslash rho\_c\; =\; \backslash frac$. Since the constant $G$ is known and the expansion rate $H$ can be measured by observing the speed at which distant galaxies are receding from us, $\backslash rho\_c$ can be determined. Its value is currently around . The ratio of the actual density to this critical value is called Ω, and its difference from 1 determines the geometry of the universe: corresponds to a greater than critical density, , and hence a closed universe. gives a low density open universe, and Ω equal to exactly 1 gives a flat universe. The Friedmann equation above can now be rearranged as follows: :$\backslash fracH^2\; =\; \backslash rho\; a^2\; -\; \backslash frac$ :$\backslash rho\_c\; a^2\; -\; \backslash rho\; a^2\; =\; -\; \backslash frac$ :$(\backslash Omega^\; -\; 1)\backslash rho\; a^2\; =\; \backslash frac.$ The right hand side of this expression contains only constants, and therefore the left hand side must remain constant throughout the evolution of the universe. As the universe expands the scale factor $a$ increases, but the density $\backslash rho$ decreases as matter (or energy) becomes spread out. For the standard model of the universe which contains mainly matter and radiation for most of its history, $\backslash rho$ decreases more quickly than $a^2$ increases, and so the factor will decrease. Since the time of the Planck era, shortly after the Big Bang, this term has decreased by a factor of around $10^,$〔 and so must have increased by a similar amount to retain the constant value of their product. 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「Flatness problem」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.