The Universe
This domain covers cosmology: the expansion of the universe, the Big Bang model and its evidence, the composition of the cosmos, and its history and fate. Questions test whether you can distinguish expansion of space from motion through space and whether you can use Hubble's law quantitatively.
Expansion and Hubble's law
- v = H₀d, with H₀ near 70 km/s/Mpc. Redshift z = Δλ/λ; cosmological redshift results from space stretching, not from galaxies plowing through space.
- The scale factor a(t) grows with time; redshift relates to it by 1 + z = 1/a.
- The Hubble time 1/H₀ gives a rough age; the actual age is 13.8 billion years, longer because expansion was decelerating early and accelerating now.
Big Bang evidence
- Cosmic microwave background at 2.725 K, released at recombination about 380,000 years after the Big Bang, showing a nearly perfect blackbody with 1-in-100,000 anisotropies.
- Primordial nucleosynthesis in the first minutes produced about 75% hydrogen, 25% helium by mass, plus deuterium and lithium - matching observed abundances.
- Distant galaxies look younger and more clustered; quasars and active galactic nuclei are common only at high redshift.
Composition and fate
- About 68% dark energy, 27% dark matter, 5% ordinary baryonic matter. Dark energy drives accelerating expansion.
- Geometry is close to flat; inflation explains flatness, horizon uniformity, and the absence of magnetic monopoles.
- Olbers' paradox is resolved by a finite age and an expanding universe.
Worked example
A galaxy has a recessional velocity of 7,000 km/s. Using H₀ = 70 km/s/Mpc, d = v/H₀ = 7,000/70 = 100 Mpc, about 326 million light-years. Now estimate the Hubble time: 1/H₀ = (3.086 × 10¹⁹ km/Mpc)/(70 km/s) = 4.41 × 10¹⁷ s, and dividing by 3.156 × 10⁷ s/yr gives 1.40 × 10¹⁰ years, about 14 billion years - close to, and slightly larger than, the true 13.8-billion-year age because of the expansion history.
Traps that cost marks
- The Big Bang is not an explosion into pre-existing space; space itself expands.
- The CMB is relic radiation from recombination, not starlight.
- Dark energy and dark matter are different: one accelerates expansion, the other clusters gravitationally.
- High redshift does not mean high peculiar velocity for cosmological distances.
- The universe has no observable edge or center in the standard model.