Cosmology is the study of the universe as a whole — its origin, structure, evolution, and ultimate fate. From the Big Bang to dark energy, from the cosmic microwave background to the large-scale structure, cosmology is one of the most precisely tested areas of physics.
Describe the sequence of cosmic epochs from inflation through BBN, recombination, and reionization.
Interpret CMB acoustic peaks to extract the curvature, baryon density, and matter density of the universe.
Quantify the Hubble tension and evaluate proposed resolutions including systematic errors and new physics.
CO.1 The Expanding Universe
Hubble (1929) discovered that galaxies recede with velocity v = H₀ d — the universe is expanding. In general relativity, the FLRW metric describes a homogeneous, isotropic universe:
where a(t) is the scale factor (a = 1 today) and k = −1, 0, +1 for open, flat, closed geometry. The Hubble parameter H(t) = ȧ/a; today H₀ ≈ 70 km/s/Mpc.
Redshift z relates the observed to emitted wavelength: 1 + z = a_obs/a_emit = 1/a(t_emit). Cosmological redshift is not a Doppler effect but the stretching of photon wavelengths by the expanding space.
CO.2 The Friedmann Equations
Substituting FLRW into Einstein's equations gives the Friedmann equations:
Density parameters: Ω_i = ρ_i/ρ_c. Current values (Planck 2018): Ω_m ≈ 0.315 (matter: 5% baryonic + 27% dark), Ω_Λ ≈ 0.685 (dark energy), k = 0 (flat).
Definition CO.1 — ΛCDM — The Standard Model of Cosmology
Lambda−ColdDarkMatter(\LambdaCDM):flatuniversewithcosmologicalconstantΛ(darkenergy,w = −1)andcolddarkmatter.Sixfreeparameters:H0,Ωbh2,Ωch2,As,ns,τ.FitsCMBAO,weaklensing,supernovaetoremarkableprecision.Tensions:Hubble(5σ),S8(matterfluctuationamplitude,2–3σ),possiblyhintingatextensions.Despiteitssuccess,\LambdaCDMtells us nothing about what dark matter or dark energy actually are.
CO.3 Cosmic History
The universe cools as it expands: T ∝ 1/a ∝ (1+z). Key epochs:
t ∼ 10⁻³⁵ s: Inflation — exponential expansion driven by inflaton field. Solves the flatness, horizon, and monopole problems. Generates primordial perturbations with spectrum P(k) ∝ k^(n_s−1), n_s ≈ 0.965 (nearly scale-invariant, Planck 2018).
t ∼ 1 s – 3 min: Big Bang Nucleosynthesis (BBN) — T falls to ∼1 MeV. Free neutrons freeze out (n/p ≈ 1/7). Protons and neutrons fuse: p + n → d + γ, then ²H + ²H → ³He + n → ⁴He + γ. Final abundances: ⁴He: 25% by mass, ²H/H ≈ 2.5×10⁻⁵, ³He/H ≈ 10⁻⁵, ⁷Li/H ≈ 10⁻¹⁰. Predicted from one parameter (baryon-to-photon ratio η): match with observed primordial abundances is a triumph of Big Bang cosmology.
t ∼ 380,000 yr: Recombination — T ≈ 3000 K. Electrons and protons combine to form neutral hydrogen. Universe becomes transparent. Relic photons today: CMB at T₀ = 2.7255 K.
t ∼ 10⁸ yr: Reionization — first stars and quasars reionize the intergalactic medium. Absorption spectra of distant quasars show the Gunn-Peterson trough.
The CMB is a near-perfect blackbody at T₀ = 2.7255 K with tiny anisotropies δT/T ∼ 10⁻⁵. The angular power spectrum C_l (variance per multipole l) shows:
Acoustic peaks: the primordial plasma was a photon-baryon fluid. Pressure waves (sound) oscillated until recombination. Modes caught at maximum compression/rarefaction appear as peaks at l ≈ 200, 500, 800... The first peak location θ ∼ 1° determines the curvature: flat universe. The peak heights determine Ω_b (baryons) and Ω_m (total matter).
Polarization: CMB is polarized (E and B modes). B-modes from primordial gravitational waves would confirm inflation — not yet detected.
CO.5 Dark Matter and Dark Energy
Dark matter evidence: galaxy rotation curves (flat, not Keplerian decline), galaxy cluster mass vs. temperature/lensing discrepancy, BBN (Ω_b = 0.049 ≪ Ω_m = 0.315), CMB peak heights, large-scale structure formation. Dark matter must be: cold (non-relativistic), non-baryonic, collisionless. Candidates: WIMPs (100 GeV−TeV scale), axions (μeV scale), sterile neutrinos, primordial black holes. No direct detection yet.
Dark energy: Ω_Λ = 0.685, equation of state w = P/(ρc²) ≈ −1 (consistent with Λ). The cosmological constant problem: why is Λ ≈ 10⁻¹²³ × (Planck scale)? The worst prediction in physics. Alternatives: quintessence (w(t) varies), phantom energy (w < −1, leads to Big Rip), modifications of gravity.
Definition CO.2 — Common Traps
Expansion is metric expansion: galaxies are not flying through pre-existing space from a central explosion.
Redshift has multiple causes: cosmological, Doppler, and gravitational shifts are conceptually distinct.
Critical density is a benchmark: it does not mean the universe is spatially small or large by itself.
Lookback time is not distance: cosmology has several useful distance measures.
2.Explain how inflation solves the horizon problem, flatness problem, and monopole problem. What observational signatures of inflation have been confirmed?
Intermediate
3.Explain baryon acoustic oscillations (BAO) as a cosmological standard ruler. What is the BAO scale and how is it used to measure dark energy?
Intermediate
4.Describe the growth of structure from linear perturbation theory to N-body simulations. What determines the shape of the matter power spectrum P(k)?