Evidence for the Big Bang —— “大爆炸理论”的证据
此贴源于前版主的悬赏贴：http://www.astronomy.com.cn/bbs/thread-169930-1-1.html 该文献的原始出处：http://www.talkorigins.org/faqs/astronomy/bigbang.html#humphreys#humphreys 以下为该文献的目录结构，内容大致上如此，有些名词实在查不到专有翻译，所以只能自己编了。希望爱好者中的专业人士能予以修正。“引言”部分，主要是对大爆炸理论的一个简单介绍，和大家在网上看到的一些科普性文章有相似之处，所以这里就不贴出译文了。随后，我会尽快完成剩余的翻译。今天先贴出第一部分“什么是大爆炸理论”。· 0) Introduction 引言oa) Purpose of this FAQ设置常见问题的目的ob) General outline 概要oc) Further sources for information 相关文献· 1) What is the Big Bang theory? 什么是大爆炸理论？oa) Common misconceptions about the Big Bang 公众对大爆炸理论的误解ob) What does the theory really say? 大爆炸理论的真正含义oc) Contents of the universe宇宙所含之物od) Summary: parameters of the Big Bang Theory总结：大爆炸理论的参数· 2) Evidence 证据oa) Large-scale homogeneity大尺度均质性ob) Hubble diagram哈勃图oc) Abundances of light elements 轻元素丰度od) Existence of the Cosmic Microwave Background Radiation 宇宙微波背景辐射oe) Fluctuations in the CMBR 宇宙微波背景辐射的波动of) Large-scale structure of the universe 宇宙的大尺度结构og) Age of stars 恒星年龄oh) Evolution of galaxies 星系演化oi) Time dilation in supernova brightness curves 超新星光度曲线中的时间膨胀oj) Tolman tests 托尔曼效应ok) Sunyaev-Zel'dovich effect桑尼耶夫–沙多维契效应ol) Integrated Sachs-Wolfe effect 萨克斯–沃尔夫积分效应om) Dark Matter 暗物质on) Dark Energy暗能量oz) Consistency 一致性· 3) Problems and Objections 问题与缺点oa) "Something can not come out of nothing" - the first law of thermodynamics“万物皆有出处”-热力学第一定律ob) The highly ordered universe today could not have come from an explosion - the second law of thermodynamics 爆炸不能创生有序的宇宙-热力学第二定律oc) Atheistic theory 无神论od) Stars older than universe? 恒星早于宇宙？oe) Arp Arp模型of) Tifft Tifft模型· 4) Alternative cosmological models 可能的宇宙模型oa) Steady state and Quasi-steady state 稳定与准稳的状态ob) MOND 修正的牛顿动力学oc) Tired light 光线老化od) Plasma cosmology 等离子宇宙oe) Humphreys Humphreys模型of) Gentry Gentry模型· 5) Open Questions 待议问题oa) The origin of the universe 宇宙的起源ob) Flatness and horizon 平坦与视界oc) Matter-antimatter asymmetry 物质与反物质间的不对称od) "Small"-scale structure 小尺度结构· 6) Summary and outlook 总结与展望· References 参考· Acknowledgments 致谢 本帖最后由 seanwillian 于 2012-1-29 14:27 编辑（红色部分有些是看不明白，猜测之意。有些是找不到合适的说法，未翻译。但这些应该不影响文章的阅读。）1) What is the Big Bang theory?什么是大爆炸理论a) Common misconceptions about the Big Bang公众对大爆炸理论的误解 In most popularized science sources, BBT is often described with something like "The universe came into being due to the explosion of a point in which all matter was concentrated." Not surprisingly, this is probably the standard impression which most people have of the theory. Occasionally, one even hears "In the beginning, there was nothing, which exploded." 在大多数流行的科学资料中，大爆炸理论通常被描述为“宇宙开端于一个无限浓缩的物质质点的爆炸”。意料之中，大多数人对大爆炸理论的第一印象可能就是这样的。偶尔，某些人甚至觉得是“宇宙开端于爆炸，在此之前，一无所有”。 There are several misconceptions hidden in these statements: · The BBT is not about the origin of the universe. Rather, its primary focus is the development of the universe over time. · BBT does not imply that the universe was ever point-like. · The origin of the universe was not an explosion of matter into already existing space. 在上述的描述中有如下几种误解： BBT并不是研究宇宙的起源，而是着眼于宇宙在整个时间尺度上的发展变化 BBT从未明确指出宇宙曾经是个质点 宇宙不是物质质点向现存空间爆炸喷放物质而形成的 The famous cosmologist P. J. E. Peebles stated this succinctly in the January 2001 edition of Scientific American (the whole issue was about cosmology and is worth reading!): "That the universe is expanding and cooling is the essence of the big bang theory. You will notice I have said nothing about an 'explosion' - the big bang theory describes how our universe is evolving, not how it began." (p. 44). The March 2005 issue also contained an excellent article pointing out and correcting many of the usual misconceptions about BBT. 著名宇宙学家P. J. E. Peebles在2001年1月的Scientific American（该杂志主题宇宙学，非常值得一读）杂志上发表简短评论：“宇宙的扩张与冷却才是大爆炸理论的本质。你应该知道我从未提过‘爆炸’。大爆炸理论描述的是我们宇宙的进化过程，而非起源。”2005年3月同样刊出的一篇优秀论文则指出并纠正了很多常见的误解。 Another cosmologist, the German Rudolf Kippenhahn, wrote the following in his book "Kosmologie fuer die Westentasche" ("cosmology for the pocket"): "There is also the widespread mistaken belief that, according to Hubble's law, the Big Bang began at one certain point in space. For example: At one point, an explosion happened, and from that an explosion cloud travelled into empty space, like an explosion on earth, and the matter in it thins out into greater areas of space more and more. No, Hubble's law only says that matter was more dense everywhere at an earlier time, and that it thins out over time because everything flows away from each other." In a footnote, he added: "In popular science presentations, often early phases of the universe are mentioned as 'at the time when the universe was as big as an apple' or 'as a pea'. What is meant there is in general the epoch in which not the whole, but only the part of the universe which is observable today had these sizes." (pp. 46, 47; FAQ author's translation, all emphasizes in original) 另一位宇宙学家，德国人，Rudolf Kippenhahn在他名为"Kosmologie fuer die Westentasche"（口袋里的宇宙）的书中写道：“最常见的误解是基于哈勃定律推测而来的宇宙开端于一个质点。比如：如果一点发生爆炸，就像我们在地球上能看到的那些一样，那么爆炸物将逐渐减薄并扩张到很大的空间中。这样的理解是不对的。哈勃定律仅仅指明物质在早期是及其浓密的，减薄和扩张只是因为所有物质在做各向同性的运动。”在脚注中，他还写道：“在主流的科学表述中，宇宙早期的形态被形容成一个‘苹果’或‘豌豆’。这种形容所要表达的是在某个时间点上我们现在的宇宙仅仅是其一部分而非全部。” Finally, the webpage describing the ekpyrotic universe (a model for the early universe involving concepts from string theory) contains a good recounting of the standard misconceptions. Read the first paragraph, "What is the Big Bang model?". 最后，描述“火宇宙理论（一个使用弦理论的关于早期宇宙的模型）”的网页上对于这些误解的更佳叙述。 There are a number of reasons that these misconceptions persist in the public mind. First and foremost, the term "Big Bang" was originally coined in 1950 by Sir Fred Hoyle, a staunch opponent of the theory. He was a proponent of the competing "Steady State" model and had a very low opinion of the idea of an expanding universe. Another source of confusion is the oft repeated expression "primeval atom". This was used by Lemaitre (one of the theory's early developers) in 1927 to explain the concept to a lay audience, albeit one that would not be familiar with the idea of nuclear bombs for a few decades to come. With these and other misleading descriptions endlessly propagated by otherwise well-meaning (and not so well-meaning) media figures, it is not surprising that many people have wildly distorted ideas about what BBT says. Likewise, the fact that many in the public think the theory is rather ridiculous is to be expected, given their inaccurate understanding of the theory and the data behind it. 公众观点中的那些误解主要来自于以下的原因：首先，“Big Bang”的说法是1950年反对“大爆炸理论”的名为Fred Hoyle先生提出的。他坚持“稳定宇宙模型”，对宇宙扩张学说评价很低。另一个混淆的来源是再三被提及的“太古原子”。这个词最先是Lemaitre（大爆炸理论早期的一个研究者）在1927年用来向公众解释概念的，当然大家不知道十几年后原子弹的概念。因为这样或那样的误导和有意无意的媒体图形传播，毫无疑问，非常多的人会对大爆炸理论的本质产生错误的理解和概念。同时，可以预期公众只会认为大爆炸理论是荒诞可笑的，进而错误的理解理论与其后的数据。
b) What does the theory really say?大爆炸理论的真正含义 Giving an accurate description of BBT in common terms is extremely difficult. Like many modern scientific topics, every such attempt will be necessarily vague and unsatisfying as certain details are emphasized and others swept under the rug（此句未翻译）. To really understand any such theory, one needs to look at the equations that fully describe the theory, and this can be quite challenging. That said, the quotes by Peebles and Kippenhahn should give one an idea of what the theory actually says. In the following few paragraphs, we will elaborate on their basic description. 要想用通俗易懂的话来解释BBT是很困难的。要想真正理解“大爆炸”理论，最好是去看看能完整描述该理论的方程组，只是这太难了点。上述的由Peebles与Kippenhahn所做的文摘应该能让人明了这个理论要讲什么。在接下来的篇幅中，我们对此详细阐述。 The simplest description of the theory would be something like: "In the distant past, the universe was very dense and hot; since then it has expanded, becoming less dense and cooler." The word "expanded" should not be taken to mean that matter flies apart -- rather, it refers to the idea that space itself is becoming larger. Common analogies used to describe this phenomenon are the surface of a balloon (with galaxies represented by dots or coins attached to the surface) or baking bread (with galaxies represented by raisins in the expanding dough). Like all analogies, the similarity between the theory and the example is imperfect. In both cases, the model implies that the universe is expanding into some larger, pre-existing volume. In fact, the theory says nothing like that. Instead, the expansion of the universe is completely self-contained. This goes against our common notions of volume and geometry, but it follows from the equations. Further discussion of this question is found in the What is the Universe expanding into? section of Ned Wright's FAQ. BBT最简单的描述就是“在遥远的过去，宇宙是极其得致密与高温，某刻之后宇宙开始逐步地扩张，也逐渐地松散与冷却”。对于单词“expanded”，不是指物质四散飞开的意思，而是指空间本身变大了。对于此现象，通常是用气球表面扩张或面包被烘焙膨胀的例子来类比的（星系则类比为气球上的斑点或贴在上面的硬币，或面团上的葡萄干）。作为一种类比，理论与例子之间的相似性并不完美。上面的两个例子中，模型表达的是宇宙确实膨胀变大了，但占据的空间是确实已经存在的空间。然而，宇宙的膨胀所占据的空间是自身。这与我们对空间几何的认识有所抵触，但它满足方程。关于这个问题的升入讨论可参考Ned’s Wright常见问答中的章节：“What is the University expanding into”（宇宙空间膨胀去哪了）。
People often have difficulty with the idea that "space itself expands". An easier way to understand this concept is to think of it as the distance between any two points in the universe increasing (with some notable exceptions, as discussed below). For example, say we have two points (A and B) which are at fixed coordinate positions. In an expanding universe, we would find two remarkable things to be true. First, the distance between A and B is a function of time and second, the distance is always increasing. “空间自身膨胀”这个概念，一般人很难理解。不过你可以把他看作是宇宙中任意两点之间距离的增加。举个例子来说，现在有固定坐标的两点A和B，当宇宙扩张膨胀时，我们会得到两个事实：一是AB两点间距与时间有确定的函数关系；二是距离增加是必然的。To really understand what this means and how one would define "distance" in such a model, it is necessary to have some idea of what Einstein's theory of General Relativity (GR) is about -- another subject that does not easily lend itself to simple explanations. One of the most popular GR textbooks by Misner, Thorne & Wheeler summarize it thusly: "Space tells matter how to move, matter tells space how to curve." Of course, this statement omits certain details of the theory, like how space also tells electromagnetic radiation how to move (demonstrated most beautifully by gravitational lensing -- the deflection of light around massive objects), how space also curves in response to energy, and how energy can cause space to do much more than simply curve. Perhaps a better (albeit longer) way of describing GR would be something like: "Energy determines the geometry and changes in the geometry of the universe, and, in turn, the geometry determines the movement of energy". 要想真正理解这个概念，以及“distance”在模型中的定义，我们得对爱因斯坦的广义相对论有所理解。而这又是很难用简单的文字解释的。关于GR的流行书籍中，由Misner, Thorne & Wheeler撰写的一书中总结说“空间决定物质的运动方式，而物质决定空间的弯曲方式”。当然，这个表示略去很多详细的内容，比如空间可以决定电磁辐射的运动方式（引力透镜就是最好的示例，光线在大质量物质周围的偏折），空间如何因能量而产生弯曲，而能量又如何能够让空间做出如此不同于寻常的弯曲。或许，广义相对论的最佳表述应该是这样的：“能量决定并改变宇宙的几何结构，相应，宇宙的结构亦决定能量的运动与分布”。
So, given this, how does one get BBT from GR? The basic equations for BBT come directly from Einstein's GR equation under two key assumptions: First, that the distribution of matter and energy in the universe is homogeneous and, second, that the distribution is isotropic. A simpler way to put this is that the universe looks the same everywhere and in every direction. The combination of these two assumptions is often termed the cosmological principle. Obviously, these assumptions do not describe the universe on all physical scales. Sitting in your chair, you have a density that is roughly 1000 000 000 000 000 000 000 000 000 000 times the mean density of the universe. Likewise, the densities of things like stars, galaxies and galaxy clusters are well above the mean (although not nearly as much as you). Instead, we find that these assumptions only apply on extremely large scales, on the order of several hundred million light years. However, even though we have good evidence that the cosmological principle is valid on these scales, we are limited to only a single vantage point and a finite volume of the universe to examine, so these assumptions must remain exactly that. 那么，怎么从GR中推导出BBT呢？BBT的基本方程式是直接从GR方程中推导得来的，其过程要求了两个假设：一是物质与能量在宇宙中的分布是均匀的；二，分布具有各项同性。简而言之就是宇宙无论任何方向的任何位置看起来都是一模一样的。这两条假设的结合也经常被称作为宇宙准则。很明显，假设仅在某些物理尺度上描述宇宙。坐在椅子上时，你的密度大概是宇宙平均密度的1000 000 000 000 000 000 000 000 000 000倍。同样的，诸如恒星，星系，星系团等，其密度也高于平均密度（当然离你的密度还是有很大差距的）。因此，我们认为假设仅在数百万光年这样的极大尺度上有效。然而，即便我们有足够的证据表明宇宙准则在这些尺度上始终成立，依然只有有限的空间可以被检测，毕竟我们能检测的时空有限。所以，这些假设必须严格成立才行。
If we adopt these seemingly simple assumptions, the implications for the geometry of the universe are quite profound. First, one can demonstrate mathematically that there are only three possible curvatures to the universe: positive, negative or zero curvature (these are also commonly called "closed", "open" and "flat" models). See these lectures on cosmology and GR and this discussion of the Friedman-Robertson-Walker metric (sometimes called the Friedman-Lemaitre-Robertson-Walker metric) for more detailed derivations. Further, the assumption of homogeneity tells us that the curvature must be the same everywhere. To visualize the three possibilities, two dimensional models of the actual three dimensional spaces can be helpful; the figure below from the NASA/WMAP Science Team gives an example. The most familiar model with positive curvature is the surface of a sphere. Not the full three dimensional object, just the surface (you can tell that the surface is two dimensional since you can specify any position with just two numbers, like longitude and latitude on the surface of the Earth). Zero curvature can be modeled as a simple flat plane; this is the classical Cartesian coordinates that most people will remember from school. Finally, one can imagine negative curvature as the surface of a saddle, where parallel lines will diverge from each other as they are projected towards infinity (they remain parallel in a zero curvature space and converge in a positively curved space). 如果接受这些看上去很简单的假设，这就意味着宇宙的结构就蕴含其中。首先，通过数学推导可以证明宇宙只能有三类曲率：正，负，零（也被称为封闭宇宙，开放宇宙，平坦宇宙）。对此想了解更多内容的读者可以去阅读一些关于宇宙学与广义相对论，以及Friedman-Robertson-Walker metric的相关文献。此外，均相的假设表明曲率必须处处相等。为了形象的描述三种情况，下面给出由NASA/WMAP Science Team绘制的三维空间的二维模型图：对于正曲率，我们最熟悉的模型就是球面。零曲率则模化为一个平板，其符合笛卡尔坐标系。最后，负曲率情况，我们可以把它想象为一个马鞍面。马鞍面上的平行线会逐渐分散，投影则趋近无穷。（这些线在零曲率面上则始终保持平行，而在正曲率面上则会汇聚）There are more complicated examples of these geometries, but we will skip discussing them here. Those interested in reading more on this point can look at this description of topology of the universe. 关于其几何形式，当然还有其它更复杂的例子，这里就不再赘述。有兴趣的读者可以去看topology of the universe.（宇宙拓扑学）。 The second main conclusion that we can draw from the cosmological principle is that the universe has no boundary and has no center. Obviously, if either of these statements were true, then the idea that all points in the universe are indistinguishable (i.e. the universe is isotropic) would be false. This conclusion can be counter-intuitive, particularly when considering a universe with positive curvature like that of a spherical shell. This space is clearly finite, but, as is also clear after a moment's thought, it is also possible to travel an arbitrarily large distance around the sphere without leaving the surface. Hence, it has no boundary. For the flat and negatively curved surfaces, it is clear that these cases must extend to infinite size. Remarkably, given the vast differences that these cases present for the geometry and size of the universe, determining which of these three cases holds for our universe is actually still an open question in cosmology. 在宇宙准则中，我们能得到的第二条结论是：宇宙既无边界亦无中心。很明显，无论哪个陈述是对的，都意味着宇宙中各点无差别的想法是错误的。这个推论似乎违反直觉，尤其是认为具有正曲率的宇宙像个球壳时。无疑，这个宇宙是有限的，但是稍经思考，就能知道任意距离的两点，都可以到达，根本就不用离开表面。也即，它是无界的。而对于零，负曲率宇宙，很明显，这两种几何构型本身就是无界的。尽管这三种构型多构建的宇宙差异巨大，但到底哪一种才能真正构建我们的宇宙的构型是宇宙学中仍有争议的一个课题。 c) Contents of the universe宇宙所含之物 As we said above, GR tells us that the matter and energy content of the universe determines both the present and future geometry of space. Therefore, if we want to make any predictions about how the universe changes over time, we need to have an idea of what types of matter and energy are present in the universe. Once again, applying the cosmological principle simplifies matters considerably. In fact, if the distribution of matter and energy is uniform on very large scales, then all we need to know is the density and pressure of each component. Even better, for most of the cases that are relevant for cosmology, the pressure and density tend to be related by a so-called "equation of state". Thus, if we know the density of a given component, then we know its pressure via the equation of state and can calculate how it will affect the geometry of the universe now and at any time in the past or future. 上文说到，广义相对论表明宇宙中的物质与能量从始至终都决定着空间的几何构型。因此，想要预测宇宙随时间的变化，首先得知道宇宙中现在含有那些物质与能量。这里，我们再一次应用宇宙准则简化物质。事实上，如果物质与能量真的在大尺度上分布均匀，那么我们所需明了的就是它们各组分的密度与压力。更进一步地讲，对于宇宙中绝大部分情况而言，压力与密度满足所谓的“状态方程”。因此，只要我们能测到特定组分的密度，就能通过状态方程计算对应的压力，进而就能计算出该组分在现在以及过去的每个时刻是如何影响宇宙的几何结构的。
After a great deal of theoretical and observational work, there are essentially three broad categories of matter and energy that we need to consider 经过大量的理论研究与实际观测，我们认为从本质上讲，宇宙中的物质与能量主要有三类是需要考虑的： · Matter: In the normal course of life on Earth, we tend to think of the relationship between pressure and density of matter as important, but incomplete. From basic chemistry or physics classes, we learn that pressure is also typically a function of temperature. Another way to think of temperature is as a measure of the speed that matter is travelling, albeit in an unordered, random manner (think of the air molecules in a balloon; they move around rapidly inside the balloon, but the balloon itself remains motionless). While these molecules may move quickly by our standards, compared to the speed of light (which is what is relevant when we consider GR) these particles are effectively motionless. To a very good approximation, we can simply set the pressure for matter to zero; what we are really saying is that the pressure is tiny compared to the energy density of the matter. · 物质：通常情况下，我们倾向于认为在物质的压力与密度之间的关系较为重要，但不完全。物理或化学基础课程阐述压力其实也是温度的函数。对于温度，有另一种描述，即：温度是物质运动速度的度量，即使速度是随机无序的（想象一下气球里面的空气分子，这些分子在气球中快速的运行，但气球本身却是静止的）。按我们的理解，空气分子运动速度非常快，但和光速相比，它们也算是静止不动的。简单设定物质的压力为零是个不错的近似。说这么多的意思就是相比于物质的密度，压力非常之小。
In cosmological parlance, this class of matter is generically described as "cold matter", a term that would include stars, planets, asteroids, interstellar dust, and so on. Since we are limited to observing photons from the rest of the universe, the fact that much of this cold matter does not glow in any appreciable way means that we have to observe it indirectly, mainly by its gravitational effect on matter that we can see. This sort of dark matter (mainly planets, burned out stars and cold gas) is quite abundant in the universe.
在宇宙学术语中，这一类物质一般称为“冷物质”，包括恒星，行星，小行星，星际尘埃等等。因为我们受限于只能通过光子进行观测，而事实上很多冷物质也不辐射可被感知的光线，导致我们只能通过它们以引力方式对可观测物质的影响来观测。这类暗物质（主要是行星，燃尽的恒星以及冷气云）在宇宙中存在的性当广泛。
In addition to this normal dark matter, there is also ample evidence that the universe contains a great deal of dark matter that is fundamentally different from the dark matter described above. While normal matter will glow if sufficiently heated, this dark matter is dark because it does not interact with light at all. This is contrary to our everyday experience, of course, but current quantum field theory predicts the existence of a number of particles that would fit this requirement (e.g. the "neutralino" predicted by supersymmetry or the "axion"; see below for more details).
除了这些普通暗物质之外，仍有足够的证据表明宇宙中还存在着大量与上文提到的暗物质不同的其他类暗物质。足够热的物质必然会发出光线，但这类暗物质之所以称为暗物质因为它压根就不与光线发生任何相互作用。这与我们日常经验相抵触，但现代量子场论预测到存在满足这种特性的粒子。（例如，超对称性预测的中微子，或者轴子）
Like in the case of the normal dark matter (which is generically called "baryonic dark matter" since it is mostly made of protons and neutrons, which belong to a particle group called "baryons"), we do not need to know the exact details of this dark matter in order to make cosmological predictions. All we do need to know is its equation of state. "Cold Dark Matter" would consist of massive, slow-moving particles, where "massive" is relative to the mass of particles like the proton and "slow" is relative to the speed of light. Like the cold baryonic matter, the pressure associated with these particles would be effectively zero. On the other hand, if the dark matter particles are very light, then they would tend to move very quickly and their associated pressure would no longer be negligible. This sort of dark matter is called "Hot Dark Matter". For completeness, one could also imagine a third, intermediate case ("Warm Dark Matter"). Finally, it is worth noting that, since it does not interact with light, the "temperature" of the dark matter is not going to have anything to do with the overall temperature of the universe; Hot Dark Matter remains hot no matter how cold the universe gets. As we will discuss later on, current observations indicate that the matter component of the universe is dominated by Cold Dark Matter, with small amounts of baryonic matter and little to no Warm or Hot Dark Matter.
像常规暗物质（也称作“重子暗物质”，因为这类暗物质主要由属于“重子”范畴的质子与中子构成）一样，我们没必要在详细了解这种暗物质之后再去做出预测，只要能了解到它的状态方程即可。“冷暗物质”主要由质量相比于质子大得多，且运动速度远小于光速的粒子构成。比如冷态重子物质，与之相关的压力可以看成是零。换言之，如果暗物质的粒子质量较轻，运动速度极快，那么它的压力就不能被忽略。对应上文的“冷暗物质”，这类则被称为“热暗物质”。为了更完备的描述，我们还可以假象第三种物质，介于冷热两者之间的“暖暗物质”。最后，既然它不与光线发生关系，那就和宇宙的温度没什么关系了。无论宇宙有多冷，热暗物质始终都是热的。后文的讨论会提及当前的观测均表明宇宙中物质的组份主要由冷暗物质，以及少量重子物质和些许不冷不热的暗物质构成。
· Radiation: Strictly speaking, this category only includes electromagnetic radiation. However, Hot Dark Matter often gets grouped together with radiation since, as the particles are moving very close to the speed of light, they have essentially the same equation of state. For radiation, the pressure is equal to one third of the energy density. From observations, we know that radiation is not a significant part of the energy density budget of the universe today. However, because of the equation of state, the energy density of radiation scales inversely as the fourth power of the size of the universe. For example, if we go back in time to the point where the observable universe was half the size it is today, we would find that the energy density was 16 times the current value, while the energy density of matter was only 8 times its value today. The clear implication here is that, no matter what their values today, if we go back far enough in time, radiation will be the dominant source of energy density in the universe. This has enormous implications for both the creation of the light elements in the very early stages of the universe (also known as primordial nucleosynthesis) and the formation of the Cosmic Microwave Background Radiation (CMBR).
辐射。严格来讲，这个类别仅涉及电磁辐射。热暗物质经常因辐射而聚集，与粒子在亚光速状态下运动时一样，因为两者的状态方程在本质上是一样的。对于辐射，压力等于能量密度的三分之一。从观测数据中，我们认为辐射在当前的宇宙能量密度中并非主要构成部分。然而状态方程中的辐射对应的能量密度与宇宙的尺度的四分之一次方成反比。简言之，如果宇宙倒退至只有现有尺寸一半时，能量密度是当前值的16倍，而物质对应的能量密度只有当前值的8倍，也就是说，无论这些数值现在是多少，只有时间倒退得足够多，辐射总归会成为能量密度的主要来源。这强烈地暗示了宇宙早期（原初核合成时期）的轻元素合成与宇宙微波背景辐射（CMBR）的形成。
· The third component of the standard picture of BBT is also the one we know the least about. The generic term for this piece is dark energy, although this term covers a very diverse array of possibilities. From quantum field theory, we know that all of space should be filled with energy, even if there is no matter or radiation present. This energy is known by various names: "zero-point energy", "zero-point fluctuations", "vacuum energy", "vacuum fluctuations", etc. As some of the names imply, this energy does not persist in the way that normal matter or radiation does; instead the particles carrying it pop in and out of existence, as predicted by Heisenberg's uncertainty principle. This sort of energy cannot be detected directly, but measurements of, e.g. the Casimir effect, demonstrate that it does exist.
BBT标准蓝图中的第三个组成部分我们仍然知之甚少。这一范畴的专有属于为“暗能量”，涵盖了多种不同的可能构成。量子场论指出任何一个空间内即便没有物质与辐射，也必然被能量充满。这种能量有称作“零点能”的，也有称为“零点波动”的，还有“真空能”和“真空波动”等称谓。从名字上就能看出来，这种能量不像常见的物质与能量那样稳定存在，而是像海森堡测不准原理预测的那样随粒子突然的涌出和消散。这种不能被直接观测到，但Casimir效应确实证明了它是真实存在的。
Taking this as an indicator that this sort of energy exists, we can explore what effect this might have from a cosmological standpoint. Regardless of the expansion of the universe, the zero-point energy density remains constant and positive. This leads to the rather curious (and non-intuitive) conclusion that the pressure associated with dark energy is negative. If one plugs a component like this into the standard BBT equations, the effect of the negative pressure is larger than that of the positive energy density. As a result, in a universe driven by dark energy, the effect of its gravity is to accelerate the expansion of the universe, instead of slowing it down (as one would expect for a universe with just matter in it).
将这种效应是为零点能量的指示器，我们能研究它能对现有的宇宙学产生什么样的影响。若不考虑宇宙的膨胀，零点能密度将是一个正常数，而这带来一个奇特的结论就是暗能量的压力是负值。如果将这一组成导入标准BBT方程组，负压力的效应将远远大于正的能量密度所能引起的效应。其结果就是由暗能量主导的宇宙会因引力作用而加速膨胀而非减速（这和假定宇宙仅有物质时的结果一样）。
One also often hears the term "cosmological constant" associated with dark energy. In order to understand the reason for this, one has to know a bit about the history of applying GR to the whole universe. When Einstein first tried to do that, he found that it predicted the universe should either expand or contract. But in Einstein's times, the universe was thought to be static. So he looked again at the assumptions which he made in deriving the equations of GR. One of them was that an empty universe, i.e., one which contains no matter or energy, should have zero curvature ("flat" as mentioned above). Einstein found that if he dropped that assumption, an additional free parameter appeared in the equations of GR. If that parameter is set to a particular value, the equations indeed yield the static universe expected back then! Accordingly, he called that additional parameter the "cosmological constant".
另一个我们常听到的与暗能量相关的术语是“宇宙常数”。要想了解这些，首先我们得先了解一下广义相对论在宇宙学中的应用历史。当爱因斯坦将广义相对论应用到宇宙中时，他发现宇宙要么膨胀要么收缩，但当时大家都认为宇宙是静止不变的。因此他回过头来又仔细研究了一下在推导广义相对论方程的过程中所作的假设。其中一个假设就是宇宙空无一物，既无物质也无能量，是个零曲率空间（也就是平坦）。爱因斯坦发现如果将这条假设去除，广义相对论方程中就会出现一个自由变量，而将其设定为某个特定值时，稳定的静止宇宙就能被推导出来。相应的，爱因斯坦将其称为“宇宙常数”。
Obviously, this was a rather ad hoc solution to an only apparent problem (made especially unnecessary when evidence began to show that the universe was not static). According to Gamow, Einstein later called this trick "his greatest blunder". That said, we now also know that empty space, without "ordinary" (or even exotic) matter and energy, still has to contain the vacuum fluctuations predicted by quantum field theory. In other words, even "empty" space still contains energy and therefore does not have to be flat. This (sort of) justifies using the cosmological parameter; in this interpretation, it would represent the "vacuum energy density" caused by quantum fluctuations, turning the cosmological constant into a particular type of dark energy. From this viewpoint, introducing the cosmological constant was not a blunder - more like accidentally discovering a necessary, even crucial additional parameter in the equations of GR and accordingly also the equations of the BBT.
很明显，这只能算是表面问题（尤其是在有证据表明宇宙并非一成不变时）的一个特解。按伽莫夫的说法，爱因斯坦后来称这个乌龙为“他最大的失误”。现在我们知道，即便一个空的空间，不含任何常规（或者奇异）物质和能量，也含有量子场论所确认的真空零点能。换句话说，空的空间也会含有能量，并因其而卷曲。在这段解释中，宇宙常数更像是一种暗能量的特例，毕竟它在方程中能表示出因量子波动而产生的“真空零点能”的效应。从这个观点上讲，引入宇宙常数算不上是个失误，更像是意外发现了广义相对论方程和BBT方程的一个必要条件，或者是一个至关重要的附加参数。 d) Summary: parameters of the Big Bang Theoryd）总结：BBT理论的主要参数 Like every physical theory, BBT needs parameters. Drawing from what we have established so far, we have 和所有物理理论一样，BBT理论也需要参数，讲了这么多，我们可以提炼出一下的主要参数： · The curvature of space. As we discussed above, this is either positive (closed), negative (open) or zero (flat). · 空间曲率。 如上文所述，空间曲率要么正（封闭），要么负（开放），要么是零（平坦）。 · The scale factor. One of the first things one notices when studying cosmology is that measuring the absolute value of any particular quantity can be extremely challenging. Rather, most of the quantities that cosmologists try to measure are actually ratios. The scale factor is the ratio between the current "size" of the universe and the size of the universe at some point in the past or future ("size" being defined as is appropriate for a given curvature). Obviously, this parameter is one today and less than one at any time in the past for an expanding universe. · 尺度因子。初学宇宙学时，人们总是首先认识到要想测量某些量的绝对数值是很困难的。相反，宇宙学家想测量的大多数量实际上都是一个相对值或比值。尺度因子就是当前宇宙的尺寸与某个时间点上宇宙尺寸之比（这个尺寸在不同的曲率条件定义不同）。很显然，这个数值在今天就是1，如果宇宙是膨胀的，那么今天之前的任何时刻，该数值都必然小于1。
· The Hubble Parameter. This is often confused with the "Hubble Constant". Partly, this is a relic from Hubble's original work showing the expansion of the universe, where it was just a fitting parameter to translate velocity into distance. In modern usage, that term only refers to the current value; in actuality this quantity varies over time. Formally, the Hubble parameter measures the rate of change of the scale factor at a given time (the derivative of the scale factor normalized by the current value). A simpler way to think about it is that the Hubble Parameter tells one how fast the universe is expanding at any particular moment. · 哈勃参数。这个概念经常会与哈勃常数产生混淆。事实上，这个参数只是哈勃将速度转换为距离的过程所使用的一个拟合参数，因历史而遗留下来，在某种程度上可以表达宇宙的扩张速度。在现代，该术语仅指当前值，因为它随时间变化。规范地讲，哈勃参数表示尺度因子在给定时刻的变化率（也即尺度因子以当前值为准归一化后对时间的一阶导数）。通俗地讲就是哈勃参数表示宇宙在指定时刻扩张得有多快。 · Deceleration Parameter. In a matter-only universe, the expansion of the universe would be slowed down by the self-gravitation of the matter, possibly even enough to cause the universe to collapse. This means that the expansion rate (the Hubble Parameter) would change and the deceleration parameter quantified that rate of change (the second derivative of the scale factor, for those keeping track). The first clue that Dark Energy was important to cosmology came from the discovery that the deceleration parameter was not negative (as expected), but actually positive. Hence, instead of slowing down, the expansion was actually accelerating. Ironically, this has led cosmologists to mostly ignore this parameter in favor of the next set of parameters. · 减速参数。在仅含物质的宇宙中，宇宙的膨胀会因物质间的引力作用逐渐减速，甚至会引起宇宙的坍缩。这意味着扩张速度（哈勃参数）是会变的，而减速参数则量化这种变化（就是尺度因子的按同样处理后的二阶导数）。自从发现减速参数是正数之后，宇宙学家开始重视暗能量。也由此，宇宙膨胀实际还是在加速而非减速。有意思的是，这使得大部分学者略去减速参数转而青睐于下一个参数。 · Component densities. Very simple here; just how much radiation, matter (baryonic and dark) and dark energy is there in the universe? These densities are usually expressed in ratios between the density in a given component and the density it would take to make the curvature of the universe flat. If one knows the values of these densities and the Hubble parameter at a particular time, then one can determine the value of the deceleration parameter; hence, the disappearance of that parameter from much of the cosmological literature in the last several years. · 组份密度。这个很简单，就是宇宙中到底有多少辐射，物质（包括重子与暗物质）和暗能量。这些密度通常表示为一种比值，即给定组分的密度与满足宇宙曲率平坦的密度值之比。如果知道这些密度值和特定时间的哈勃参数，那么就能确定减速参数，这就是为什么这些参数在最近几年宇宙学文献中消失的原因。
· Dark Energy Equation of State. As mentioned above, for radiation and matter the equations of state are determined by known physics. For dark energy, however, the data is still not up to the challenge of picking a preferred model. As such, most papers in the literature treat the dark energy equation of state as a free parameter (possibly varying with time, depending on the model) or explicitly choose a value as a prior constraint (see below). · 暗能量状态方程。已有的物理学知识能够描述辐射与物质的状态方程。对于暗能量，目前尚无足够的数据以构建有效的方程。就这点而论，大部分文献或者将暗能量的状态方程视为一个自由变量（可能随时间变化，取决于模型的设定），或者明确地选择一个特定数值作为先验约束（参考下文）。
This seems like a long list of parameters -- so many that one might argue that any theory with this many knobs might be tuned to fit any set of observations. However, as mentioned above, they are not really independent. Choosing a value for the Hubble parameter immediately affects the expected values for the densities and the deceleration parameter. Likewise, a different mix of component densities will change the way that the Hubble parameter varies over time. In addition, there is a wide variety of cosmological observations to be made -- observations with wildly different methodologies, sensitivities and systematic biases. A consensus model has to match all of the available data and, over the last decade in cosmology, combining these experiments has resulted in what has been called the "concordance model". 这个参数列表真实够长的，可能有些人就要说：任何一个理论只要参数足够多，没什么现象不能满足的。不过我们说过了，这些参数都不是相互独立的。比如，只要哈勃参数改变了，那么减速参数和密度值就立刻有所改变。同样地，不同组分的密度也会因哈勃参数随时间的变化而做出相应变化。另外，已有的观测因观测方法，灵敏度，系统偏差而不尽相同。一个好的模型不仅能满足所有的有效数据，也能与“Hexie模型”所构建的各种实验相容。
This basic picture is built on the framework of the so-called "Lambda CDM" model. The Lambda indicates the inclusion of dark energy in the model (specifically the cosmological constant, which implies an equation of state where the pressure is equal to -1 times the energy density). "CDM" is short for "cold dark matter". Thus, the name of the model incorporates what are believed to be the two most important components of the universe: dark energy and dark matter. The respective abundances of these two components and the third important component, baryonic (or "ordinary") matter, is shown in the pie chart below (provided by the NASA/WMAP Science Team): As mentioned above, these values come from simultaneously fitting the data from a large variety of cosmological observations, which is our next topic. 下图式根据“Lambda CDM”模型的构架制作而成。“Lambda”表示模型中的暗能量部分（特指宇宙常数，暗示存在一种压力与能量密度反相的状态方程）。“CDM”是冷暗物质（Cold Dark Matter）的缩写。这两个名字的合并意味着该模型认为宇宙中最主要的两个组成部分是暗能量与暗物质。除此之外，第三重要的组分则是重子物质。三者的比例以饼图的方式列于图中。按前文所书，这些数值是根据下面将提到的各种观测值综合得到的。 这么丰富啊，辛苦LZ了。 真是好文章，辛苦楼主了。可惜我不能给你精华
个别错字，请楼主自己修改一下。 本帖最后由 seanwillian 于 2012-2-2 11:52 编辑
第二部分内容比较长，今天先发一部分：
2) Evidence2）证据Having established the basic ideas and language of BBT, we can now look at how the data compares to what we expect from the theory. As we mentioned at the end of the last section, there is no single experiment that is sensitive to all aspects of BBT. Rather, any given observation provides insight into some combination of parameters and aspects of the theory and we need to combine the results of several different lines of inquiry to get the clearest possible global picture. This sort of approach will be most apparent in the last two sections where we discuss the evidence for the two most exotic aspects of current BBT: dark matter and dark energy. 在了解了BBT的基本含义与术语后，让我们来看看理论与实践是怎么契合的。上文已经明确指出BBT任何一方面都不能靠单一的实验来表达。但是，任何观测都能在潜在的方面预示某些参数的综合结果或者BBT理论的某一方面，而我们要做的就是发掘其中的内容从不同的角度逐步的勾勒和细化理论的全景。这种逼近的方法是研究BBT理论中让人难以捉摸的暗物质与暗能量最常用的方式。
a) Large-scale homogeneity大尺度上的均质性
Going back to our original discussion of BBT, one of the key assumptions made in deriving BBT from GR was that the universe is, at some scale, homogeneous. At small scales where we encounter planets, stars and galaxies, this assumption is obviously not true. As such, we would not expect that the equations governing BBT would be a very good description of how these systems behave. However, as one increases the scale of interest to truly huge scales -- hundreds of millions of light-years -- this becomes a better and better approximation of reality. 从广义相对论中推到BBT理论时，我们设定了一个关键的基本假设：宇宙在某些尺度上是均质的。在我们能看到的行星尺度，恒星尺度，甚至星系尺度等的小尺度上，均质性是不成立的。所以，也别指望BBT理论能很好地描述这些尺度上的天体行为。但是，只要将尺度放大的足够，比如数亿光年的尺度，BBT理论就会越来越接近实际情况。
As an example, consider the plot below showing galaxies from the Las Campanas Redshift Survey (provided by Ned Wright). Each dot represents a galaxy (about 20,000 in the total survey) where they have measured both the position on the sky and the redshift and translated that into a location in the universe. Imagine putting down many circles of a fixed size on that plot and counting how many galaxies are inside each circle. If you used a small aperture (where "small" is anything less than tens of millions of light years), then the number of galaxies in any given circle is going to fluctuate a lot relative to the mean number of galaxies in all the circles: some circles will be completely empty, while others could have more than a dozen. On the other hand, if you use large circles (and stay within the boundaries!), the variation from circle to circle ends up being quite small compared to the average number of galaxies in each circle. This is what cosmologists mean when they say that the universe is homogeneous. An even stronger case for homogeneity can be made with the CMBR, which we will discuss below. 下图是拉斯坎培那斯红移巡天计划（Las Campanas Redshift Survey）所做星系红移图（由Ned Wright提供）。每个点都代表一个星系（巡天计划大概观测了2万个星系）的位置与红移量，并将其转换为图中的样子。大家可以试一下：随意在图上画几个直径一样的圆圈，看看每个圈里有几个星系。如果你选择一个小直径的圆（这里的“小”实际上按比例就是小于百万光年的尺寸），那么圈里的星系数量可能会在平均值上下剧烈波动，也即：有些圈里空无一物，有些则充满星系。相应地，如果你选的圈够大（当然圆只能画在界限之内），那么每个圈里的星系数量相对于平均值就会极为接近。这就是宇宙学家所说的宇宙是均匀的。关于宇宙是均匀的这一说法，更有效的例子是随后要讨论的宇宙微波背景辐射。http://www.talkorigins.org/faqs/astronomy/lcrs.gif
b) Hubble Diagramb) 哈勃图
The basic idea of an expanding universe is the notion that the distance between any two points increases over time. One of the consequences of this effect is that, as light travels through this expanding space, its wavelength is stretched as well. In the optical part of the electromagnetic spectrum, red light has a longer wavelength than blue light, so cosmologists refer to this process as redshifting. The longer light travels through expanding space, the more redshifting it experiences. Therefore, since light travels at a fixed speed, BBT tells us that the redshift we observe for light from a distant object should be related to the distance to that object. This rather elegant conclusion is made a bit more complicated by the question of what exactly one means by "distance" in an expanding universe (see Ned Wright's Many Distances section in his cosmology tutorial for a rundown of what "distance" can mean in BBT), but the basic idea remains the same. 宇宙扩张的基本概念是任意两点之间的距离始终随时间的增加而增加。这种效应所带来的结果之一就是光线的波长增加。在电磁谱中，红光的波长要大于蓝光，所以宇宙学家称这种效应为红移。光线穿越的距离越大，红移量也就越大。既然光速是定值，那么BBT理论要告诉我们的就是观测的红移量与发出这束光的天体距离相关。要做出更佳的表述很难，因为要对扩张宇宙中的“距离”概念做更严格的定义也是个麻烦，但本意是不变的。
Cosmological redshift is often misleadingly conflated with the phenomenon known as the Doppler Effect. This is the change in wavelength (either for sound or light) that one observes due to relative motion between the observer and the sound/light source. The most common example cited for this effect is the change in pitch as a train approaches and then passes the observer; as the train draws near, the pitch increases, followed by a rapid decrease as the train gets farther away. Since the expansion of the universe seems like some sort of relative motion and we know from the discussion above that we should see redshifted photons, it is tempting to cast the cosmological redshift as just another manifestation of the Doppler Effect. Indeed, when Edwin Hubble first made his measurements of the expansion of the universe, his initial interpretation was in terms of a real, physical motion for the galaxies; hence, the units on Hubble's Constant: kilometers per second per megaparsec. 宇宙学中的红移往往被人和多普勒效应混淆。多普勒效应是指波长因观测者与声/光源之间的相对运动而产生的变化。这种效应最常用的例子就是火车驶向或离开时音高的变化。当火车驶近时，音高变强；离去时，音高减弱。由于宇宙的扩张类似于上面提到的相对运动，我们就应该能观测到红移现象。这就会诱使我们将红移看做是多普勒效应的一个现象。但事实上，当Edwin Hubble第一次构造出宇宙扩张的测量时，他是用星系真实的物理运动来解释这些的，因此，哈勃常数的单位是“公里/（秒×百万秒差距）。
In reality, however, the "motion" of distant galaxies is not genuine movement like stars orbiting the center of our galaxy, Earth orbiting the Sun or even someone walking across the room. Rather, space is expanding and taking the galaxies along for the ride. This can be seen from the formula for calculating the redshift of a given source. Redshift (z) is related to the ratio of the observed wavelength (W_O) and the emitted wavelength of light (W_E) as follows: 1 + z = W_O/W_E. The wavelength of light is expanded at the same rate as the universe, so we also know that: 1 + z = a_O/a_E, where a_O is the current value of the scale factor (usually set to 1) and a_E is the value of the scale factor when the light was emitted. As one can see, velocity is nowhere to be found in these equations, verifying our earlier claim. More detail on this point can be found at The Cosmological Redshift Reconsidered. If one insists (and is very careful about what exactly one means by "distance" and "velocity"), understanding the cosmological redshift as a Doppler shift is possible, but (for reasons that we will cover next) this is not the usual interpretation. 然而事实上，这些疏远星系之间的“运动”并未我们通常意义上的那个“运动”，比如恒星绕星系中心运动，地球绕太阳做圆周运动，也不同于我们绕着屋子转圈。更为合理的说法是空间的膨胀拖着星系运动。这一点从红移的计算关系式上可以看出来：红移量Z与观测到的光线波长（W_O）与实际发射光线的波长（W_E）之比有关，即：1+z=W_O/W_E。既然波长的拉长速率与宇宙的扩张速率一样，那么我们可变换得到当前尺度因子a_O（一般设定为1）与被测光线发出时的尺度因子a_E的关系，即：1+z=a_O/a_E。现在大家看到了，速度项在方程中是无处不在的，也验证了前文所述。关于该问题，更详细的资料大家可以参考The Cosmological Redshift Reconsidered（再议宇宙红移）。当然，如果您坚持认为红移效应就是多普勒效应（也较真与“距离”与“速度”的准确概念），我们也没办法，毕竟靠口头解释就让您信服实在太难了。（至于为什么，我们会在下文解释）。
As we mentioned previously, even after Einstein developed GR, the consensus belief in astronomy was that the universe was static and had existed forever. In 1929, however, Edwin Hubble made a series of measurements at Mount Wilson Observatory near Pasadena, California. Using Cepheid variable stars in a number of galaxies, Hubble found that the redshift (which he interpreted as a velocity, as mentioned above) was roughly proportional to the distance. This relationship became known as Hubble's Law and sparked a series of theoretical papers that eventually developed into modern BBT. 自爱因斯坦提出广义相对论以来，大多人依然如上文提到的那样认为宇宙是静态的且永存不朽。1929年，Edwin Hubble在加州帕萨迪纳附近的威尔逊天文台，通过观测各个星系中的造父变星，进行了一系列的测量。Hubble发现红移量（他也解释为“速度”）大致上与距离成正比关系。该关系也被称为哈勃定律（Hubble Law），引发研究者撰写了一系列的论文，而这些论文最终构成现代大爆炸理论。
At first glance, assembling a Hubble diagram and determining the value of Hubble's Constant seems quite easy. In practice, however, this is not the case. Measuring the distance to galaxies (and other astronomical objects) is never simple. As mentioned above, the only data that we have from the universe is light; imagine the difficulty of accurately estimating the distance to a person walking down the street without knowing how tall they are or being able to move your head. However, using a combination of geometry physics and statistics, astronomers have managed to come up with a series of interlocking methods, known as the distance ladder, which are reasonably reliable. The TO FAQ on determining astronomical distances provides a thorough run-down of these methods, their applicability and their limitations. 乍看之下，绘制哈勃图进而确定哈勃常数不费吹灰之力。只是事与愿违。测量星系距离（或其它天体的距离）绝非易事，因为光是我们从宇宙中获取数据的唯一途径。想象一下，在不知道一个人身高或者我们不能做出任何移动的情况下，要想精确地测量一个街上散步之人离我们有多远是很困难的。不过，采用几何物理与数理统计，天文学者还是构建了一些联锁测量方法，比如已被证实可靠的“距离阶梯”方法。在FAQ on determining astronomical distances中，你可以找到各种测量方法的原理与优缺点。
Conversely, the other side of the equation, the redshift, is relatively easy to measure given today's astronomical hardware. Unfortunately, when one measures the redshift of a galaxy, that value contains more than just the cosmological redshift. Like stars and planets, galaxies have real motions in response to their local gravitational environment: other galaxies, galaxy clusters and so on. This motion is called peculiar velocity in cosmological parlance and it generates an associated redshift (or blueshift!) via the Doppler Effect. For relatively nearby galaxies, the amplitude of this effect can easily dwarf the cosmological redshift. The most striking example of this is the Andromeda galaxy, within our own Local Group. Despite being around 2 million light years away, it is on a collision course with the Milky Way and the light from Andromeda is consequently shifted towards the blue end of the spectrum, rather than the red. The upshot of this complication is that, if we want to measure the Hubble parameter, we need to look at galaxies that are far enough away that the cosmological redshift is larger than the effects of peculiar velocities. This sets a lower limit of roughly 30 million light years and even once we get beyond this mark, we need to have a large number of objects to make sure that the effects of peculiar velocities will cancel each other. 当今的硬件条件下。测量方程左侧的红移量是件简单的事。不过，我们测量的星系红移量可不仅仅只由宇宙红移量构成。像恒星与其卫星一样，星系也会因其所处的引力环境，如星系，星系团等，而产生真实运动。这种运动在宇宙学中称之为本动速度，并通过多普勒效应产生对应的红移量。如果星系靠得足够近，这种影响的幅度甚至能完全掩盖宇宙红移量。举个最明显的例子，2百万光年外与银河系同属本星系群的仙女座星系正处在与银河系碰撞过程中，它发出的光线在光谱上表现为向蓝光运动的红移，而非红光。这种复杂因素的结果就是如果想测量哈勃常数，目光就得转向那些距离足够远，宇宙红移量远大于因其它速度引起的附加红移量的星系。这也就设置一个大概的界限即3千万光年，如果观测目标不在界限之外，那么我们就得附加大量的目标进行观测，以确保能消除本动速度所带来的影响。
The combination of these two complications explain (in part) why it has taken several decades for the best measurements of Hubble's Constant to converge on a consensus value. With current data sets, the nearly linear nature of the Hubble relationship is quite clear, as shown in the figure below (based on data from Riess (1996); provided by Ned Wright). 这两个复杂的解释说明了为何数十年来哈勃常数的测量值能够集中于一个数值而被大众接受。基于当前的数据，哈勃关系中的内在线性关系十分明了，就像下图所表示的那样。（图中数据来自于Riess1996年的成果，由Ned Wright提供）。http://www.talkorigins.org/faqs/astronomy/hub_1996.gif
As mentioned previously, the standard version of BBT assumed that the dominant source of energy density for the last several billion years was cold, dark matter. Feeding this assumption into the equations governing the expansion of the universe, cosmologists expected to see that the expansion would slow down with the passage of time. However, in 1998, measurements of the Hubble relationship with distant supernovae seemed to indicate that the opposite was true. Rather than slowing down, the past few billion years have apparently seen the expansion of the universe accelerate (Riess 1998; newer measurements: Wang 2003, Tonry 2003). In effect, what was observed is that the light of the observed supernovae was dimmer than expected from calculating their distance using Hubble's law. 标准BBT模型假定在过去的数十亿年中低温的暗物质是能量密度的主导来源。那么将该假设导入描述宇宙扩张的方程所得结果使得宇宙学家认为随时间的推移宇宙扩张会逐步减慢。然而在1998年，对部分深空中的超新星进行哈勃关系式验证观测的结果却给出相反的结论：在过去的几十亿年中宇宙的扩张不但没减速反而加速了（Riess1996测量，最新测定由Wang和Tonry在2003年分别完成）。实际的测定是从超新星观测的光线强度比采用哈勃定律根据距离所计算结果要低。
Within standard BBT, there are a number of possibilities to explain this sort of observation. The simplest possibility is that the geometry of the universe is open (negative curvature). In this sort of universe, the matter density is below the critical value and the expansion will continue until the effective energy density of the universe is zero. The second possibility is that the distant supernovae were artificially dimmed as the light passed from their host galaxies to observers here on Earth. This sort of absorption by interstellar dust is a common problem with observations where one has to look through our own galaxy's disk, so one could easily imagine something similar happening. This absorption is usually wavelength dependent, however, and the two teams investigating the distant supernovae saw no such effect. For the sake of argument, however, one could postulate a "gray dust" that dimmed objects equally at all wavelengths. The final possibility is that the universe contains some form of dark energy (see sections 1c and 2n). This would accelerate the expansion, but could keep the geometry flat. 采用标准BBT理论，这种现象的可能解释有很多。最简单的解释是宇宙的几何结构是开放式的（负曲率）。在这种宇宙中，物质密度要低于临界值，扩张运动将持续到有效能量密度达到零值。其次可能的解释为远方的超新星光线在穿过所属星系到达地球上观测者的过程中被某些原因减光削弱了。光线穿越星际尘埃时因吸收而减弱是很常见的事情，尤其是我们要在银河星系盘方向观测目标时。所以大家不难想象。这种吸收与光线的波长有关，但有两支研究团队的研究结果表明对于这些超新星观测而言没有出现这种影响。因为争论的缘故，部分人假设存在“灰色星尘”可以在所有波长上产生消光作用。最后一种可能行就是宇宙中存在一种类似暗能量的物质（参见章节1c和2n）。这种物质既能加速宇宙扩张有能满足宇宙平坦的要求。
At redshifts below unity (z < 1), these possibilities are all roughly indistinguishable, given the precision available in the measurements. However, for a universe with a mix of dark matter and dark energy, there is a transition point from the domination of the former to the latter (just like the transition between the radiation- and matter-dominated expansion prior to the formation of the CMBR). Before that time, dark matter was dominant, so the expansion should have been decelerating, only beginning to accelerate when the dark energy density surpassed that of the matter. This so-called cosmic jerk implies that supernovae before this point should be noticeably brighter than one would expect from a open universe (constant deceleration) or a universe with gray dust (constant dimming). New measurements at redshifts well above unity have shown that this "jerk" is indeed what we see -- about 8 billion years ago our universe shifted from slowly decelerating to an accelerated expansion, exactly as dark energy models predicted (Riess 2004). 若红移量低于单位值（z<1），这些可能的解释在允许的精度下能被大致的分辨出来。然而对于同时存在暗物质与暗能量的宇宙而言，应该存在一个决定两者谁处于主导地位的转换点（如同CMBR从辐射主导到物质主导的变换）。在转换点之前，暗物质起主导作用，那么宇宙扩张应该是减速状态直到暗能量密度超越按物质密度才会转入加速状态。这种情况被称作“宇宙阶跃”（cosmic jerk），预示着在此点之前的超新星将显著地比从开放宇宙（持续减速）中或含有“灰色星尘”宇宙（常量消光）中观测到的光线要亮。而今新的红移量测量明显高于单位值，也就是说80亿年前我们的宇宙从缓慢的减速状态中转入了加速扩张阶段，就像暗能量模型预测的那样。
c) Abundances of light elements轻元素丰度As we mentioned previously, standard BBT does not include the beginning of our universe. Rather, it merely tracks the universe back to a point when it was extremely hot and extremely dense. Exactly how hot and how dense it could be and still be reasonably described by GR is an area of active research but we can safely go back to temperatures and densities well above what one would find in the core of the sun. 如前文所述标准BBT理论并不包括宇宙起源问题。相反，它仅仅是追溯宇宙至一个足够热和致密的时刻。至于到底有热和致密到什么程度，现在还是个活跃的研究课题，尽管可以用广义相对论使当地予以描述。但我们确实可以追溯至那个温度与密度都远远高于太阳内部的时期。
In this limit, we have temperatures and densities high enough that protons and neutrons existed as free particles, not bound up in atomic nuclei. This was the era of primordial nucleosynthesis, lasting for most of the first three minutes of our universe's existence (hence the title of Weinberg's famous book "The First Three Minutes"). A detailed description of Big Bang Nucleosynthesis (BBN) can be found at Ned Wright's website, including the relevant nuclear reactions, plots and references. For our purposes a brief introduction will suffice. 鉴于如此，我们将温度和密度设定到保证中子和质子可以作为自由粒子存在，而不被束缚在原子核内。这就是原初核合成时期，在我们的宇宙出现后最初三分钟（因此，Weinberg的著作名为“最初三分钟”）。关于大爆炸核合成，在Ned Wright的网站上有更详细的说明，包括了相关的核反应，图表和参考文献。在本文中简单的介绍就足够了。
Like in the core of our Sun, the free protons and neutrons in the early universe underwent nuclear fusion, producing mainly helium nuclei (He-3 and He-4), with a dash of deuterium (a form of hydrogen with a proton-neutron nucleus), lithium and beryllium. Unlike those in the Sun, the reactions only lasted for a brief time thanks to the fact that the universe's temperature and density were dropping rapidly as it expanded. This means that heavier nuclei did not have a chance to form during this time. Instead, those nuclei formed later in stars. Elements with atomic numbers up to iron are formed by fusion in stellar cores, while heavier elements are produced during supernovae. Further information on stellar nucleosynthesis can be found at the Wikipedia pages and in section 2g below. 就像在太阳的核心一样，那些存在于早期宇宙中的自由中子和质子通过聚变反应生成的大量氦原子（氦3和氦4），以及少量的氘（氢的一种同位素，包含一个中子和一个质子），锂和铍。因为宇宙扩张，温度与密度迅速下降，这样的反应仅持续了很短的时间。这意味着重元素没有机会出现。相应的，重元素是在恒星内部形成的。按原子序数向上直到铁元素，都是在恒星内部通过聚变合成的，再往后的重元素则通过超新星爆炸形成。恒星核合成的信息可以在维基百科和2g章看到。
Armed with standard BBT (easier this time since we know the expansion at that time was dominated by the radiation) and some nuclear physics, cosmologists can make very precise predictions about the relative abundance of the light elements from BBN. As with the Hubble diagram, however, matching the prediction to the observation is easier said than done. Elemental abundances can be measured in a variety of ways, but the most common method is by looking at the relative strength of spectral features in stars and galaxies. Once the abundance is measured, however, we have a similar problem to the peculiar velocities from the previous section: how much of the element was produced during BBN and how much was generated later on during stellar nucleosynthesis? 综合标准BBT与一些核物理，宇宙学家能够根据BBN准确地预测出轻元素的相对丰度。与哈勃图一样，将理论值与观测值对应起来是说着容易做着难。元素丰度可以通过很多方法进行测量，更为通行的方式为测量恒星与星系的光谱。不过就算测到了元素丰度，我们还有一个类似如前文所言的关于速度的问题，即：有多少是在BBN阶段合成的，又有多少是在恒星核合成过程中产生。
To get around this problem, cosmologists use two approaches: 为了解决这个问题，宇宙研究者选择其它两条路径：· Deuterium: Of the elements produced during BBN, deuterium has by far the lowest binding energy. As a result, deuterium that is produced in stars is very quickly consumed in other reactions and any deuterium we observe in the universe is very likely to be primordial. The downside of this approach is that primordial deuterium can also be destroyed in the outer layers of stars giving us an underestimate of the total abundance, but there are other methods (like looking in the Lyman alpha forest region of distant quasars) which avoid these problems. 氘：在BBN过程中生成的轻元素中，氘所需的结合能最小。因此，恒星内部生成的氘原子很快就会被其它核反应消耗掉，这样我们所观测到的氘原子就很有可能是最原始的那一批。这种近似的缺点就是原初氘原子在恒星的外层也会被消耗，进而导致数值的低估。不过现在有一些方法（比如Lyman alpha forest region of distant quasars，远类星体的拉曼α森林）可以解决这些问题。
· Look Deep: One can try to look at stars and gas clouds which are very far away. Thanks to the finite speed of light, the larger the distance between the object and observers here on Earth, the more ancient the image. Hence, by looking at stars and gas clouds very far away, one can observe them at a time when the heavy element abundance was much lower. By going far enough back, one would eventually arrive at an epoch where no prior stars had had a chance to form, and thus the elemental abundances were at their primordial levels. At the moment, we cannot look back that far. These objects would have very high redshifts, taking the light into the infrared where observations from the ground are made very difficult by atmospheric effects. Likewise, the great distance makes them extremely dim, adding to our problems. Both of these problems should be helped greatly when the James Webb Space telescope enters service. What we can do now is to observe older stars, measure their elemental abundances, and try to extrapolate backwards. 望远：这条路就是放眼望向宇宙的深处，观测那些遥远的恒星与气云。幸好光速是有限的，天体与我们的距离越远，我们所观测的图像就越古老。因此，通过观测宇宙深处的恒星与气云，我们能观测到重元素丰度极低的时间。如果观测的足够远，最终能观测到恒星尚未形成的时期，并观测原始元素丰度比。当然现在，我们还看不到那么远。这些观测目标都有很高的红移，目标谱线处在红外区。由于大气的影响，这些光谱在地面上直接进行观测是非常困难的。同样，由于距离遥远，星光黯淡，更加难以被观测到。这些问题在James Webb空间望远镜服役之后就能迎刃而解了。现在我们能做的就是观测这些性对古老的恒星，测量元素丰度并想办法将结果外推。
Like most BBT predictions, the primordial element abundance depends on several parameters. The important ones in this case are the Hubble parameter (the expansion speed determines how quickly the universe goes from hot and dense enough for nucleosynthesis to cold and thin enough for it to stop) and the baryon density (in order for nucleosynthesis to happen, baryons have to collide and the density tells us how often that happened). The dependence on both parameters is generally expressed as a single dependence on the combined parameter OmegaB h2 (as seen in the figure below, provided by Ned Wright). 和BBT所做出的其它预测一样，原初元素丰度取决于多个参数。最重要的几个参数是哈勃常数（也即宇宙扩张速度，表达宇宙以能够发生核合成过程的热与致密为起始到冷却至完全停止扩张的速度）和重子密度（重子只有碰撞才能发生核合成反应，而密度能告诉我们核合成的发生频率）。对这两个参数的依赖性一般变换为对一个综合参数，OmegaBh2，的依赖性。http://www.talkorigins.org/faqs/astronomy/abundance.gif
As this figure implies, there is a two-fold check on the theory. First of all, measurements of the various elemental abundances should yield a consistent value of OmegaB h2 (the intersection of the horizontal bands and the various lines). Second, independent measurements of OmegaB h2 from other observations (like the WMAP results in 2e) should yield a value that is consistent with the composite from the primordial abundances (the vertical band). Both approaches were used in the past; before the precise results of WMAP for the baryon density, the former was used more often. For a detailed account of the state of knowledge in 1997, look at Big Bang Nucleosynthesis Enters the Precision Era. 如图所示，理论提供了两种校验方式。其一为：各种元素丰度的测量值应当给出一个一致的OmegaB h2值（水平带与丰度变化线的交点）；其次为：不同观测，多次独立测量得到的OmegaB h2值应当给出一个与各种元素丰度综合值一致的结果（垂直带）。过去，这两种方法都有人使用。不过在WMAP给出重子密度的准确值后之前，前者用得较多。详细内容，可以参考Big Bang Nucleosynthesis Enters the Precision Era.
One of the major pieces of evidence for the Big Bang theory is consistent observations showing that, as one examines older and older objects, the abundance of most heavy elements becomes smaller and smaller, asymptoting to zero. By contrast, the abundance of helium goes to a non-zero limiting value. The measurements show consistently that the abundance of helium, even in very old objects, is still around 25% of the total mass of "normal" matter. And that corresponds nicely to the value which the BBT predicts for the production of He during primordial nucleosynthesis. For more details, see Olive 1995 or Izotov 1997. Also look at the plot below, comparing the prediction of the BBT to that of the Steady State model (data taken from Turck-Chieze 2004, plot provided by Ned Wright). 大爆炸理论的另一个主要证据就是重元素与氦元素丰度的预测值与观测值一致。在观测中可以得到越是古老的天体，其含有的重元素丰度就越小，随着时间的前推，丰度逐渐接近于零，而氦元素则接近于一个非零数值。测量表明即便是最古老的天体，氦元素也占“常规”物质总量的25%，极为接近BBT理论针对原初核合成过程中氦元素含量所做出的预测值。如果想了解更多，请阅读Olive 1995 or Izotov 1997。下图为稳定宇宙模型与BBT理论的预测值与观测值的对比，很明显BBT理论更接近于事实（图中数据摘自文献Turck-Chieze 2004，由Ned Wright绘制）。 http://www.talkorigins.org/faqs/astronomy/He-vs-O.gif
Recent calculations as well as references to recent observations can be found in Mathews (2005). In earlier studies, there were some problems with galaxies which had apparently very low helium abundances (specifically I Zw 18); this problem was addressed and resolved in the meantime (cf. Luridiana 2003). 近期根据观测进行的计算，可参阅文献。在早期研究者中存在部分星系（尤其是I Zw 18）氦元素含量过低问题，但这些已经被解决（Luridiana 2003）。
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