📚 A2 Physics: Cosmology Key Points | 宇宙学考点精讲
Welcome to the complete revision guide for A2 Physics Cosmology. This article covers all essential concepts, from redshift and Hubble’s law to cosmic microwave background and dark energy, ensuring you are fully prepared for your examinations.
欢迎阅读A2物理宇宙学的完整复习指南。本文涵盖所有核心概念，从红移、哈勃定律到宇宙微波背景辐射和暗能量，帮助你为考试做好充分准备。
1. Introduction to Cosmology | 宇宙学简介
Cosmology is the branch of astronomy that deals with the origin, evolution, and eventual fate of the universe. The universe is isotropic and homogeneous on large scales, a concept known as the Cosmological Principle. This means the universe looks the same in all directions and has no preferred center.
宇宙学是天文学的一个分支，研究宇宙的起源、演化和最终命运。在大尺度上，宇宙是各向同性和均匀的，这就是宇宙学原理。这意味着宇宙在各个方向看起来都一样，没有特殊中心。
The observable universe is limited by the distance light has traveled since the Big Bang. Studying distant objects allows us to look back in time, providing evidence for the universe’s expansion.
可观测宇宙受限于自大爆炸以来光所走过的距离。研究遥远天体让我们能够回溯时间，为宇宙膨胀提供证据。
2. Doppler Effect and Redshift | 多普勒效应与红移
The Doppler effect for light causes a shift in wavelength when a source moves relative to an observer. If a galaxy moves away, the light is stretched to longer wavelengths, known as redshift. For speeds much less than the speed of light, redshift z is given by:
光的Doppler效应会导致光源相对于观察者运动时波长的移动。如果星系远离，光波被拉伸至更长波长，称为红移。当速度远小于光速时，红移 z 由下式给出：
z = Δλ / λ₀ ≈ v / c (v ≪ c)
where Δλ = λ_obs – λ₀, λ₀ is the rest wavelength, v is the recession speed, and c is the speed of light. A positive z indicates a redshift; a negative z would be a blueshift (approaching source). In cosmology, virtually all distant galaxies exhibit redshift, showing they are receding.
其中 Δλ = λ_obs – λ₀，λ₀ 是静止波长，v 是退行速度，c 是光速。正 z 值表示红移；负 z 值表示蓝移（靠近的光源）。在宇宙学中，几乎所有遥远星系都显示红移，表明它们正在远离。
For high-speed objects, the relativistic Doppler formula must be used. However, the simple linear relation is sufficient for most A2 calculations.
对于高速物体，必须使用相对论多普勒公式。然而，对于大多数A2计算，简单的线性关系就足够了。
3. Hubble’s Law | 哈勃定律
Edwin Hubble discovered that the recession velocity v of a galaxy is directly proportional to its distance d from us. This relationship is known as Hubble’s Law:
埃德温·哈勃发现，星系的退行速度 v 与它离我们的距离 d 成正比。这一关系称为哈勃定律：
v = H₀ d
where H₀ is the Hubble constant, typically given in units of km s⁻¹ Mpc⁻¹. Current measurements place H₀ around 70 km s⁻¹ Mpc⁻¹. This law implies the universe is expanding uniformly, with every galaxy moving away from every other galaxy.
其中 H₀ 是哈勃常数，通常以 km s⁻¹ Mpc⁻¹ 为单位。当前的测量结果 H₀ 约为 70 km s⁻¹ Mpc⁻¹。该定律表明宇宙在均匀膨胀，每一个星系都在彼此远离。
The Hubble constant can be used to estimate the age of the universe. If the expansion rate has been constant, the age t ≈ 1/H₀. This yields roughly 13.8 billion years, consistent with other measurements.
哈勃常数可用于估算宇宙的年龄。如果膨胀速率一直恒定，年龄 t ≈ 1/H₀。这大致得到 138 亿年，与其他测量一致。
4. Distance Measurement and the Cosmic Distance Ladder | 距离测量与宇宙距离阶梯
Accurate distance measurements are essential for determining Hubble’s constant. Astronomers use a “cosmic distance ladder” of overlapping methods:
精确的距离测量对于确定哈勃常数至关重要。天文学家使用一系列相互衔接的“宇宙距离阶梯”方法：
- Parallax – for nearby stars. The apparent shift of a star against distant background as Earth orbits the Sun. Distance d (in parsecs) = 1/p (parallax angle p in arcseconds).
- Cepheid Variables – pulsating stars with a well-defined period-luminosity relation. Their intrinsic brightness is known from the period, so apparent brightness gives distance. Used for galaxies up to ~30 Mpc away.
- Type Ia Supernovae – exploding white dwarfs that reach a consistent peak luminosity. They serve as standard candles for much greater distances, allowing measurement of the Hubble constant and the discovery of accelerating expansion.
视差法 – 用于近距恒星。地球绕太阳公转时，恒星相对于遥远背景的视移动。距离 d（秒差距）= 1 / 视差角 p（角秒）。
造父变星 – 具有明确周期-光度关系的脉动变星。其内在亮度由周期确定，因此通过视亮度可获得距离。可用于最远约 30 Mpc 的星系。
Ia型超新星 – 爆发白矮星达到一致峰值亮度。它们作为更远距离的标准烛光，允许测量哈勃常数并发现宇宙加速膨胀。
The combination of these methods calibrates the distance–redshift relation and refines H₀.
这些方法的结合校准了距离-红移关系并完善了 H₀。
5. The Big Bang Theory | 大爆炸理论
The Big Bang theory states that the universe began from an extremely hot, dense singularity about 13.8 billion years ago and has been expanding ever since. The expansion is not an explosion into pre-existing space but the stretching of space itself.
大爆炸理论认为，宇宙大约在 138 亿年前从一个极热、极密的奇点开始，并一直膨胀至今。这种膨胀不是向现有空间的爆炸，而是空间本身的拉伸。
Key evidence for the Big Bang includes:
大爆炸的关键证据包括：
- The redshift of galaxies (Hubble’s law) – all distant galaxies recede.
- The cosmic microwave background (CMB) – remnant heat from the early universe.
- The abundance of light elements (hydrogen, helium, lithium) – matches predictions from Big Bang nucleosynthesis.
星系的红移（哈勃定律）——所有遥远星系都在远离。
宇宙微波背景辐射（CMB）——早期宇宙的残余热量。
轻元素（氢、氦、锂）的丰度——与大爆炸核合成的预言相符。
6. Cosmic Microwave Background | 宇宙微波背景辐射
Approximately 380,000 years after the Big Bang, the universe cooled enough for electrons and protons to combine into neutral hydrogen – an event called recombination. Photons decoupled from matter and streamed freely. This relic radiation, now redshifted into the microwave region, is the CMB.
大爆炸后约 38 万年，宇宙冷却到足以使电子和质子结合成中性氢——这一事件称为复合。光子与物质退耦，自由传播。这种遗迹辐射，现已红移到微波波段，就是CMB。
The CMB has a nearly perfect blackbody spectrum at a temperature of about 2.725 K. Tiny temperature fluctuations (anisotropies) of order 10⁻⁵ correspond to density variations that later formed galaxies and large-scale structure.
CMB具有近乎完美的黑体谱，温度约为 2.725 K。微小的温度涨落（各向异性），量级为 10⁻⁵，对应于后来形成星系和大尺度结构的密度变化。
The uniformity of the CMB supports the Cosmological Principle and provides a snapshot of the infant universe.
CMB的均匀性支持宇宙学原理，并提供了婴儿宇宙的快照。
7. Dark Matter and Dark Energy | 暗物质与暗能量
Observations of galaxy rotation curves and gravitational lensing indicate there is much more mass in galaxies than we can see. This unseen mass is called dark matter. It does not emit, absorb, or reflect electromagnetic radiation, but its gravitational effects are evident. Dark matter makes up about 27% of the total energy density of the universe.
星系旋转曲线和引力透镜的观测表明，星系中的质量远多于我们所见。这种看不见的质量称为暗物质。它不发射、不吸收、不反射电磁辐射，但它的引力效应很明显。暗物质约占宇宙总能量密度的 27%。
Even more mysterious is dark energy, which constitutes about 68% of the universe. Discovered through observations of distant Type Ia supernovae, dark energy is responsible for the accelerating expansion of the universe. It acts as a repulsive force counteracting gravity on cosmic scales.
更神秘的是暗能量，它约占宇宙的 68%。通过对遥远Ia型超新星的观测发现，暗能量导致宇宙加速膨胀。它充当了在宇宙尺度上与引力相抗衡的排斥力。
The remaining ~5% is ordinary baryonic matter – the atoms that make up stars, planets, and us.
剩下的约 5% 是普通重子物质——构成恒星、行星和我们的原子。
8. The Fate of the Universe | 宇宙的最终命运
The ultimate destiny of the universe depends on its total density relative to the critical density. The density parameter Ω is defined as the ratio of actual density to critical density. The three possible scenarios are:
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