Cosmology Study Guide

📖 Core Concepts Physical Cosmology – Treats the universe as a whole, merging mathematics with observations (e.g., CMB, supernovae). Big Bang Model – Universe began in a hot, dense state → expansion & cooling; supported by Hubble redshift, CMB, primordial abundances. Cosmic Inflation – Ultra‑rapid exponential expansion fractions of a second after the Big Bang; explains uniform temperature and flat geometry. ΛCDM Model – Standard framework: cosmological constant (Λ, dark energy) + cold dark matter (CDM); fits CMB, galaxy clustering, supernovae. Dark Matter vs. Dark Energy – Dark matter (≈ 26.6 % of total) clusters gravitationally; dark energy (≈ 68.5 %) drives accelerated expansion. Cosmic Microwave Background (CMB) – Relic radiation (2.73 K) with tiny temperature anisotropies; a snapshot of the universe 380 kyr after the Big Bang. Age of the Universe – $13.799 \pm 0.021$ Gyr (Planck 2014). Spatial Geometry – Closed (finite, can recollapse) vs. Open (infinite, expands forever). --- 📌 Must Remember Hubble Law (1929): $v = H0 d$ (galaxy recession speed ∝ distance). CMB Composition (Planck 2014): 4.9 % baryonic matter, 26.6 % dark matter, 68.5 % dark energy. Key Observational Milestones 1923‑24: Cepheid variables → Andromeda distance → extra‑galactic nebulae. 1964: CMB discovery → strong Big Bang evidence. Late 1990s: Type Ia supernovae → accelerating expansion. Inflation solves: horizon problem, flatness problem, monopole problem. Einstein’s Λ: Introduced 1917; later re‑interpreted as dark energy causing acceleration if Λ > 0. --- 🔄 Key Processes From Newtonian Mechanics to Relativistic Cosmology Newton → universal gravitation → Kepler’s laws. Einstein (1917) → General Relativity (GR) → dynamic spacetime models. Establishing Cosmic Expansion Friedmann (1922) derives expanding solutions from GR. Hubble measures redshifts → linear distance‑redshift relation → expansion confirmed. Inflationary Epoch Quantum fluctuations → exponential expansion (scale factor $a(t) \propto e^{Ht}$). Stretching smooths density variations → uniform CMB temperature. ΛCDM Parameter Determination CMB anisotropy spectra (Planck) → fit six base parameters (Ωb, Ωc, ΩΛ, ns, τ, H0). Complement with supernovae (distance modulus) & BAO (baryon acoustic oscillations) for consistency. --- 🔍 Key Comparisons Closed vs. Open Universe Closed: Positive curvature, finite volume, possible recollapse. Open: Zero/negative curvature, infinite volume, expands forever. Λ (Cosmological Constant) vs. Dark Energy (General) Λ: Constant energy density, equation of state $w = -1$. Dark Energy: May vary with time (e.g., quintessence), $w \lesssim -1/3$. Big Bang vs. Steady‑State (historical) Big Bang: Finite age, evolving density, CMB relic. Steady‑State: Continuous matter creation, no CMB (now disfavored). --- ⚠️ Common Misunderstandings “Inflation = Big Bang” – Inflation is a brief pre‑expansion phase; the Big Bang describes the subsequent hot, dense evolution. “Dark matter is dark energy” – Dark matter clusters gravitationally; dark energy drives acceleration and does not clump. “ΛCDM predicts a static universe” – ΛCDM includes expansion; Λ merely adds an accelerating term. Age vs. Hubble Time – Age $≈$ 13.8 Gyr ≠ $1/H0$ (≈ 14.4 Gyr) because of deceleration/acceleration history. --- 🧠 Mental Models / Intuition Balloon Analogy – Surface of an inflating balloon represents the expanding universe; galaxies are dots on the surface, moving apart as the balloon stretches, not moving through space. Frozen Sound Waves – CMB temperature peaks correspond to sound waves frozen at recombination; their spacing sets the angular scale of anisotropies. Energy Budget Pie – Visualize the universe as a pie: tiny slice (≈ 5 %) ordinary matter, larger slice (≈ 27 %) invisible matter, biggest slice (≈ 68 %) mysterious energy causing acceleration. --- 🚩 Exceptions & Edge Cases Spatial Curvature Near Zero – Observations are consistent with flat geometry (Ωk ≈ 0) but tiny positive/negative curvature remains within error bars. Dynamic Dark Energy – Current data fit Λ (constant), but future measurements could reveal a time‑varying $w$. Modified Gravity Theories – Some propose alternatives to dark energy (e.g., f(R) gravity); not part of ΛCDM but worth recognizing as “edge‑case” explanations. --- 📍 When to Use Which Redshift–Distance (Hubble Law) – Use for nearby galaxies (z ≲ 0.1) where linear approximation holds. Type Ia Supernovae – Best for measuring accelerated expansion (z ≈ 0.5–1.5) and constraining Λ. CMB Power Spectrum – Primary tool for global parameters (Ωb, Ωc, ΩΛ, ns). Gravitational Lensing – Ideal for mapping dark matter distribution in clusters and the cosmic web. --- 👀 Patterns to Recognize Exponential Growth → Flatness – Any process described by $a(t) \propto e^{Ht}$ quickly drives curvature toward zero. Temperature Anisotropy Peaks → Acoustic Oscillations – Peaks at multipole ℓ ≈ 200 correspond to sound horizon scale. Supernova Light‑Curve Stretch → Standard Candle – Uniform peak luminosity after correcting for stretch; deviations hint at new physics. --- 🗂️ Exam Traps Confusing Age with Expansion Rate – A common distractor swaps $13.8$ Gyr with $1/H0$; remember the age includes deceleration/acceleration phases. Mixing Percentages – Some choices reverse dark matter and dark energy fractions; recall: 5 % baryons, 27 % dark matter, 68 % dark energy. Inflation vs. Big Bang Timing – Options may state “inflation occurred after recombination”; correct answer: inflation preceded recombination by 10⁻³⁶ s. Closed vs. Open Geometry vs. Fate – Closed ≠ necessarily recollapse if Λ dominates; an accelerated Λ can keep a closed universe expanding forever. ---