📚 Cosmology Key Concepts: IB & OCR Physics Revision | IB OCR 物理：宇宙学考点精讲
The study of cosmology explores the origin, evolution, and ultimate fate of the universe. For IB and OCR A Level Physics students, mastering key topics such as Hubble’s law, the cosmic microwave background, and the evidence for dark energy is essential for examinations. This guide breaks down the core ideas into concise paired explanations, blending conceptual understanding with quantitative reasoning.
宇宙学研究宇宙的起源、演化和最终命运。对于 IB 和 OCR A Level 物理学生来说，掌握哈勃定律、宇宙微波背景辐射和暗能量证据等关键主题对考试至关重要。本指南将核心概念分解为简洁的配对解释，融合概念理解和定量推理。
1. Hubble’s Law and the Expanding Universe | 哈勃定律与膨胀的宇宙
Hubble’s law states that the recessional velocity v of a galaxy is directly proportional to its distance d from us: v = H₀ d, where H₀ is the Hubble constant. This linear relationship indicates that the universe is expanding uniformly.
哈勃定律指出，星系的退行速度 v 与其到我们的距离 d 成正比：v = H₀ d，其中 H₀ 是哈勃常数。这种线性关系表明宇宙正在均匀膨胀。
The Hubble constant is typically expressed in km s⁻¹ Mpc⁻¹, with a current accepted value around 70 km s⁻¹ Mpc⁻¹. Taking the reciprocal 1/H₀ yields an approximate age of the universe of about 13.8 billion years, assuming a constant expansion rate.
哈勃常数通常以 km s⁻¹ Mpc⁻¹ 表示，目前公认值约为 70 km s⁻¹ Mpc⁻¹。取倒数 1/H₀ 可以得到宇宙的近似年龄，假设膨胀速率恒定，约为 138 亿年。
Cosmological redshift z is defined as z = Δλ/λ₀, where λ₀ is the rest wavelength. For nearby galaxies (low speeds), z ≈ v/c. The redshift tells us how much the universe has expanded since light was emitted, linked to the scale factor a(t) by 1+z = a(t₀)/a(t).
宇宙学红移 z 定义为 z = Δλ/λ₀，其中 λ₀ 是静止波长。对于邻近星系（低速），z ≈ v/c。红移告诉我们自光发射以来宇宙膨胀了多少，与尺度因子 a(t) 的关系为 1+z = a(t₀)/a(t)。
2. The Cosmic Microwave Background (CMB) | 宇宙微波背景辐射
The CMB is the relic radiation from the early universe, discovered by Penzias and Wilson in 1965. It has a nearly perfect blackbody spectrum at a temperature of approximately 2.73 K. The CMB provides strong evidence for the Big Bang model.
CMB 是早期宇宙的残余辐射，由彭齐亚斯和威尔逊于 1965 年发现。它具有近乎完美的黑体谱，温度约为 2.73 K。CMB 为大爆炸模型提供了有力证据。
The tiny temperature fluctuations (anisotropies) in the CMB map correspond to primordial density perturbations that seeded galaxy formation. The peak observed at an angular scale of about 1 degree confirms the universe is spatially flat.
CMB 图中微小的温度波动（各向异性）对应于原初密度扰动，这些扰动催生了星系形成。在约 1 度角尺度上观测到的峰值证实宇宙在空间上是平坦的。
The CMB was emitted when the universe cooled enough for electrons and protons to combine into neutral hydrogen (recombination), at a temperature of about 3000 K. Since then, the expansion has stretched the radiation by a factor of roughly 1100, cooling it to the microwave region.
CMB 是在宇宙冷却到电子和质子结合成中性氢（复合）时发射的，当时温度约 3000 K。从那时起，宇宙膨胀将辐射拉伸了约 1100 倍，使其冷却到微波波段。
3. Evidence for the Big Bang | 大爆炸的证据
The three primary observational pillars of the Big Bang theory are: (1) the recession of galaxies (Hubble’s law), (2) the cosmic microwave background radiation, and (3) the relative abundances of light elements (primordial nucleosynthesis).
大爆炸理论的三个主要观测支柱是：（1）星系的退行（哈勃定律），（2）宇宙微波背景辐射，以及（3）轻元素的相对丰度（原初核合成）。
Primordial nucleosynthesis predicts that roughly 25% of the mass of ordinary matter should be helium-4, with small amounts of deuterium, helium-3, and lithium. Observations of old stars and gas clouds match these predictions.
原初核合成预测普通物质质量的约 25% 应为氦-4，还有少量的氘、氦-3 和锂。对老年恒星和气体云的观测与这些预测相符。
The expansion of the universe implies that in the past, all matter and energy were concentrated in an extremely hot, dense state. Essentially, tracing back galaxy motions leads to a singularity – the Big Bang.
宇宙膨胀意味着在过去，所有物质和能量都集中在极其炽热致密的状态。本质上，追溯星系运动会导致一个奇点——大爆炸。
4. Dark Matter and Galactic Rotation Curves | 暗物质与星系旋转曲线
Observations of spiral galaxies show that the orbital speed of stars remains roughly constant, or even rises, at large distances from the galactic centre, instead of decreasing as predicted by Newtonian gravity from visible matter. This discrepancy implies the presence of a large, invisible mass component known as dark matter.
对旋涡星系的观测表明，恒星在离星系中心很远处的轨道速度大致保持恒定甚至上升，而不是像仅由可见物质预言的牛顿引力那样下降。这种差异意味着存在大量不可见的质量成分，即暗物质。
Dark matter does not emit, absorb, or reflect electromagnetic radiation, but its gravitational effects are evident in galaxy clusters and gravitational lensing. Candidates include WIMPs (Weakly Interacting Massive Particles) and axions.
暗物质不发射、吸收或反射电磁辐射，但其引力效应在星系团和引力透镜中显而易见。候选粒子包括 WIMPs（弱相互作用大质量粒子）和轴子。
Evidence from the Bullet Cluster, where the mass distribution (from gravitational lensing) is separated from the hot gas, strongly supports the existence of non-baryonic dark matter.
子弹星系团的证据中，质量分布（来自引力透镜）与热气体分离，有力地支持了非重子暗物质的存在。
5. Dark Energy and the Accelerating Universe | 暗能量与加速宇宙
In the late 1990s, observations of Type Ia supernovae revealed that the expansion of the universe is accelerating. This acceleration requires a mysterious repulsive force termed dark energy, which makes up about 68% of the total energy density of the universe.
1990 年代末，对 Ia 型超新星的观测揭示宇宙的膨胀正在加速。这种加速需要一种神秘的斥力，称为暗能量，它约占宇宙总能量密度的 68%。
Dark energy is often associated with the cosmological constant Λ in Einstein’s field equations. It can be thought of as the energy of the vacuum itself, driving galaxies apart at an ever-increasing rate.
暗能量通常与爱因斯坦场方程中的宇宙学常数 Λ 相关联。它可以看作是真空本身的能量，驱使星系以不断加快的速度相互远离。
The equation of state parameter w = p/ρ for dark energy is close to −1, consistent with a cosmological constant. The discovery of acceleration earned the 2011 Nobel Prize in Physics.
暗能量的状态方程参数 w = p/ρ 接近 −1，与宇宙学常数一致。加速膨胀的发现获得了 2011 年诺贝尔物理学奖。
6. Redshift, Scale Factor, and the Hubble Law Details | 红移、尺度因子与哈勃定律详解
The Hubble constant measures the current rate of expansion: H₀ ≈ 70 km s⁻¹ Mpc⁻¹. A galaxy at a distance of 100 Mpc recedes at approximately 7000 km s⁻¹. The linear relationship v = H₀ d is valid for relatively small redshifts (z ≲ 0.1).
哈勃常数测量当前膨胀速率：H₀ ≈ 70 km s⁻¹ Mpc⁻¹。距离 100 Mpc 的星系以约 7000 km s⁻¹ 的速度退行。线性关系 v = H₀ d 适用于相对较小的红移（z ≲ 0.1）。
For larger redshifts, relativistic corrections become important. The cosmological redshift is a stretching of space itself, not a Doppler shift in the usual sense. The formula 1+z = a(t₀)/a(tₑ) describes how the scale factor has changed from emission tₑ to observation t₀.
对于较大的红移，相对论修正变得重要。宇宙学红移是空间本身的拉伸，而非通常意义上的多普勒频移。公式 1+z = a(t₀)/a(tₑ) 描述了从发射时刻 tₑ 到观测时刻 t₀ 尺度因子的变化。
7. The Age and Size of the Observable Universe | 可观测宇宙的年龄与大小
Using the Hubble constant, we can estimate the Hubble time t_H = 1/H₀ ≈ 14 billion years. More precise calculations incorporating the effects of dark energy and dark matter yield an age of about 13.8 × 10⁹ years.
利用哈勃常数，我们可以估算哈勃时间 t_H = 1/H₀ ≈ 140 亿年。结合暗能量和暗物质的影响进行更精确的计算，得出年龄约为 13.8 × 10⁹ 年。
The observable universe extends to a comoving distance of roughly 46 billion light-years, corresponding to the furthest light that has had time to reach us since the Big Bang. The particle horizon is the boundary of the observable universe.
可观测宇宙延伸到约 460 亿光年的共动距离，对应于自大爆炸以来有足够时间到达我们的最远光线。粒子视界就是可观测宇宙的边界。
8. The CMB Power Spectrum and Cosmological Parameters | CMB 功率谱与宇宙学参数
The CMB power spectrum shows peaks from acoustic oscillations in the early plasma. The position and amplitude of these peaks constrain parameters such as the baryon density Ω_b, cold dark matter density Ω_c, and the curvature of the universe.
CMB 功率谱显示了早期等离子体中声学振荡产生的峰值。这些峰值的位置和幅度限制了诸如重子密度 Ω_b、冷暗物质密度 Ω_c 以及宇宙曲率等参数。
The first peak at ℓ ≈ 200 implies a flat geometry (Ω_total ≈ 1). The ratio of odd to even peaks is sensitive to baryon density. These measurements are in excellent agreement with the ΛCDM model.
第一个峰位于 ℓ ≈ 200 意味着平坦几何（Ω_total ≈ 1）。奇数峰与偶数峰的比例对重子密度敏感。这些测量与 ΛCDM 模型非常一致。
9. Olbers’ Paradox and the Darkness of the Night Sky | 奥伯斯佯谬与夜空黑暗
Olbers’ paradox asks: if the universe is infinite and static, why is the night sky dark? In such a universe, every line of sight would end on a star, so the sky should be blazing bright. The paradox is resolved by the expansion of the universe and the finite age of the Big Bang, which limits the amount of starlight that has reached us.
奥伯斯佯谬问道：如果宇宙是无限且静态的，为什么夜空是黑暗的？在这样的宇宙中，每条视线最终都会落在恒星上，因此天空应当明亮耀眼。这个悖论通过宇宙的膨胀和大爆炸的有限年龄得以解决，这限制了到达我们的星光总量。
Additionally, cosmological redshift shifts the light from distant stars into the infrared, contributing to the darkness. Thus, the dark night sky supports the Big Bang model.
此外，宇宙学红移将遥远恒星的光移至红外波段，也造成了黑暗。因此，黑暗的夜空支持大爆炸模型。
10. The Ultimate Fate of the Universe | 宇宙的最终命运
The future of the universe depends on its density and the nature of dark energy. If dark energy continues as a cosmological constant, the expansion will accelerate forever, leading to a “Big Freeze.” Alternatively, if dark energy becomes dynamic, a “Big Rip” could occur, tearing apart galaxies, stars, and eventually atoms.
宇宙的未来取决于其密度和暗能量的性质。如果暗能量作为宇宙学常数持续存在，膨胀将永远加速，导致“大冻结”。或者，如果暗能量是动态的，可能发生“大撕裂”，撕裂星系、恒星乃至原子。
Measurements of the cosmic microwave background and large-scale structure indicate a flat universe with Ω_total ≈ 1, but dominated by dark energy (Ω_Λ ≈ 0.7), suggesting an eternal accelerating expansion.
对宇宙微波背景和大尺度结构的测量表明，宇宙是平坦的，Ω_total ≈ 1，但由暗能量主导（Ω_Λ ≈ 0.7），暗示永恒的加速膨胀。
11. Stellar Parallax and Distance Ladder (Related to Cosmology) | 恒星视差与距离阶梯（与宇宙学相关）
Cosmology relies on accurate distance measurements. The cosmic distance ladder starts with radar for the solar system, then stellar parallax for nearby stars, Cepheid variables for nearby galaxies, and Type Ia supernovae for distant galaxies. Hubble’s law is calibrated using standard candles.
宇宙学依赖于精确的距离测量。宇宙距离阶梯从太阳系的雷达测距开始，然后是邻近恒星的视差，附近星系的造父变星，以及遥远星系的 Ia 型超新星。哈勃定律是使用标准烛光校准的。
Parallax is the apparent shift in a star’s position due to Earth’s motion, measured in arcseconds. The distance in parsecs is d = 1/p, where p is the parallax angle. This method provides the foundation for all extragalactic distances.
视差是由于地球运动导致的恒星位置视偏移，以角秒为单位测量。距离（秒差距）为 d = 1/p，其中 p 为视差角。这种方法为所有星系外距离提供了基础。
12. Key Equations and Quantitative Examples | 关键方程与定量例子
Below are the essential equations for cosmology exams. Practice converting units: 1 Mpc = 3.09 × 10²² m, 1 year = 3.16 × 10⁷ s.
以下是宇宙学
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