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📘 How does cosmology describe the universe?

Friedmann equations, the CMB, and dark energy—how cosmology turns the whole sky into a model.

13
lessons
~30 min
to learn
Adults
level
Start the course →

What you’ll learn

  1. The FLRW Metric and Friedmann EquationsDerive the Friedmann equations from the Einstein field equations and evaluate their solutions for different density parameters.The FLRW metric encodes homogeneity and isotropy while the Friedmann equations govern expansion dynamics. Exact solutions reveal open, flat, and closed geometries tied to critical density. These relations set the quantitative framework used throughout observational cosmology.
  2. Hubble Tension and Distance Ladder CalibrationQuantify the Hubble tension and assess systematic uncertainties in local versus CMB-derived H0 values.Local distance ladder and CMB inferences disagree at high significance. Potential causes range from unmodeled systematics to new physics beyond Lambda-CDM. Current analyses emphasize cross-checks with gravitational-wave standard sirens and strong-lensing time delays.
  3. Big Bang Nucleosynthesis and Primordial AbundancesCalculate light-element yields from nuclear reaction networks and compare them with observed primordial abundances.BBN fixes the baryon density at early times and tests the standard model at MeV temperatures. Agreement for deuterium and helium supports the hot Big Bang while the lithium problem highlights possible astrophysical or particle-physics solutions. Also covers Recombination and CMB Power Spectrum: Recombination decouples photons and imprints acoustic oscillations whose amplitudes and phases depend on early-universe composition. Parameter extraction yields tight limits on curvature, dark matter density, and scalar spectral index.
  4. Cosmic Inflation and Horizon ProblemSolve the horizon and flatness problems via inflationary dynamics and derive predictions for primordial perturbations.Inflation generates nearly scale-invariant fluctuations whose statistics match CMB data. The tensor-to-scalar ratio and non-Gaussianity parameters provide direct tests of single-field slow-roll models.
  5. Dark Matter Evidence from Rotation Curves and LensingEvaluate dynamical and lensing constraints on the dark matter density profile and halo mass function.Multiple independent probes converge on collisionless cold dark matter halos whose density profiles follow NFW or Einasto forms. Baryonic feedback modulates the inner slope but leaves the overall abundance intact.
  6. Accelerated Expansion and Dark Energy Equation of StateConstrain dark energy equation-of-state parameters using distance-redshift relations and growth-rate measurements.Geometric and dynamical probes both indicate late-time acceleration driven by a component with negative pressure. Distinguishing a cosmological constant from dynamical dark energy requires percent-level control of systematics.
  7. Baryon Acoustic Oscillations as Standard RulerDerive the BAO scale from linear perturbation theory and apply it to constrain expansion history.BAO provides a calibrated comoving ruler whose redshift evolution directly maps dark energy. Combined with CMB priors it yields sub-percent constraints on curvature and dark energy density.
  8. Large-Scale Structure and Halo BiasModel galaxy clustering statistics and extract cosmological parameters from redshift-space distortions.Perturbation theory and N-body simulations predict the nonlinear power spectrum and covariance. Bias parameters and growth measurements jointly constrain modified gravity and neutrino mass.
  9. First Stars, Reionization, and 21 cm CosmologyTrace the thermal and ionization history from the dark ages through reionization using 21 cm observables.The 21 cm line probes the intergalactic medium before luminous sources dominate. Intensity mapping experiments will map fluctuations on cosmological scales and constrain the timing of reionization.
  10. Supermassive Black Holes and AGN FeedbackQuantify AGN feedback efficiency and its impact on galaxy and halo scaling relations.Black hole growth and feedback regulate the bright end of the luminosity function. Multi-wavelength observations calibrate the energy coupling that shapes the red sequence.
  11. Quantum Cosmology and the Wave Function of the UniverseCompare canonical quantum cosmology approaches and their predictions for initial conditions and singularities.Quantum gravity frameworks aim to resolve the classical singularity and select viable inflationary trajectories. Observational signatures remain speculative but motivate tests via tensor modes and non-Gaussianity.
  12. Hubble Tension Extensions and Early Dark EnergyAssess whether early-universe modifications can reconcile local and CMB Hubble constant measurements without spoiling other observables.EDE scenarios alter the sound horizon while preserving late-time expansion. They face tight constraints from BAO, weak lensing, and the CMB damping tail.
  13. Next-Generation Surveys and Cosmological ForecastsForecast parameter constraints from upcoming photometric and spectroscopic surveys and identify limiting systematics.Stage-IV surveys will test Lambda-CDM at the sub-percent level across multiple probes. Synergies between imaging and spectroscopic data will control both statistical and systematic uncertainties.

Questions this course answers

For a flat, matter-only universe the Friedmann equation integrates to which exact solution?

When Ω_m=1 and k=0 the equation ȧ² ∝ a^{-1} integrates directly to a ∝ t^{2/3}.

In a flat ΛCDM universe today, what fraction of the critical density must be dark energy if Ω_m ≈ 0.3?

Flatness requires Ω_m + Ω_Λ = 1, so Ω_Λ = 0.7 when Ω_m = 0.3.

Drag the slider to the local-ladder H0 value reported by SH0ES.

The SH0ES Cepheid-calibrated supernova sample yields 73.0 km s inverse Mpc; this is the central value that produces the 5-sigma tension with Planck.

A new strong-lensing time-delay measurement returns H0 = 71.0 plus or minus 2.0 km s inverse Mpc. Which statement correctly assesses its implication for the tension?

The 71 plus or minus 2 interval overlaps both the 67.4 and 73.0 central values, so the measurement remains compatible with either determination and does not yet resolve the discrepancy.

Using the BBN scaling, what deuterium abundance D/H would result if η were lowered by 10%?

Because D/H scales roughly as η^{-1.6} near the observed value, a 10% drop in η raises D/H by ~17%, moving the prediction from 2.55×10^{-5} to ~2.8×10^{-5}.

Why does a factor-of-three lithium shortfall not invalidate the standard BBN framework that successfully predicts deuterium and helium?

Deuterium and helium-4 together fix the baryon density and neutron lifetime at the percent level; lithium-7 is produced at the 10^{-10} level and can be depleted inside stars or modified by late decays without changing the dominant yields.

Grounded in trusted sources

  • NASA
  • ESA
  • NSF
  • NASA Wilkinson Microwave Anisotropy Probe / Planck cosmology results (public NASA summaries)
  • ESA Planck — cosmic microwave background
  • NSF — cosmic surveys

Every Wunder lesson is built from real, reputable sources — never invented.

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