Expert-level cosmology covering the Big Bang, cosmic expansion, dark matter, dark energy, CMB, large-scale structure, and observational cosmology.
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Friedmann equation: describes expansion of universe, derived from GR. Hubble law: recession velocity proportional to distance. Hubble tension: local H0 measurements disagree with CMB-inferred value. Scale factor a: ratio of proper distance to comoving distance. Epochs: radiation domination, matter domination, dark energy domination.
Evidence: rotation curves, gravitational lensing, CMB, structure formation. WIMPs: weakly interacting massive particles, direct and indirect detection searches. Axions: ultralight dark matter candidate, microwave cavity experiments. CDM: cold dark matter, non-relativistic at decoupling, forms halos. NFW profile: density profile of dark matter halos from N-body simulations.
Cosmological constant Lambda: energy density of vacuum, constant equation of state. Equation of state w: dark energy requires w less than negative one third. Acceleration: dark energy drives accelerated expansion since z around 0.4. Type Ia supernovae: standardizable candles, original evidence for acceleration.
Recombination: z around 1100, photons decouple from matter, last scattering surface. Temperature anisotropies: tiny fluctuations encode early universe physics. Power spectrum: angular power spectrum Cl vs multipole l. Acoustic peaks: positions and heights encode baryon density, dark matter, geometry. Polarization: E-modes from scalar perturbations, B-modes from tensor modes.
| Pitfall | Fix |
|---|---|
| Confusing different distance measures | Specify luminosity, angular diameter, or comoving |
| Ignoring systematic errors | Dominant over statistical in precision cosmology |
| Treating Lambda as explanation | Cosmological constant is parameterization not explanation |
| Misinterpreting Hubble tension | Check if statistical or systematic before concluding new physics |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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