Astrophysics and Cosmology
Core concepts
A candidate must be fluent in the distance ladder (parallax, main-sequence fitting, Cepheids, Type Ia supernovae), redshift and the Hubble-Lemaître law, the thermal history of the universe, nucleosynthesis, and the evidence base for dark matter and dark energy. Know the cosmic microwave background's blackbody temperature (about 2.725 K) and its acoustic peaks, the meaning of the scale factor, and the difference between luminosity distance and comoving distance.
Traps
Questions love to blur lookback time with distance, or ask for recession velocity at high redshift where the linear v = cz approximation fails. Do not confuse the Hubble constant's units (km/s/Mpc) with a velocity. Remember that cosmic expansion stretches wavelengths, so observed temperature scales as (1+z). Distinguish the particle horizon from the observable edge set by recombination.
Worked example
A galaxy shows a hydrogen line at 700 nm that has a rest wavelength of 656 nm. Redshift z = (700/656) - 1 ≈ 0.067. For small z, recession speed ≈ cz ≈ 0.067 × 3×10^5 km/s ≈ 2.0×10^4 km/s. With H0 = 70 km/s/Mpc, distance ≈ 20,000/70 ≈ 290 Mpc. Rule of thumb: at z below about 0.1, cz is a fair velocity proxy; beyond that, use a cosmological model.
Rule of thumb
For a flat matter-dominated universe, age ≈ 2/(3H0); adding dark energy raises the age toward 1/H0.