The universe on the largest scale
Cosmology studies the universe as a whole. Distances are huge, so we use special units:
- Light-year (ly): the distance light travels in one year, about 9.46 × 10¹⁵ m.
- Parsec (pc): about 3.26 ly = 3.09 × 10¹⁶ m. A megaparsec (Mpc) is a million parsecs.
Stars group into galaxies; our Milky Way holds a few hundred billion stars. Galaxies gather into groups (tens of galaxies, like our Local Group with Andromeda) and clusters (hundreds to thousands, held by gravity). Clusters join into superclusters along long filaments and sheets, around nearly empty voids. This sponge-like pattern is the cosmic web. On the very largest scales (hundreds of Mpc) the universe looks about the same everywhere and in every direction: the cosmological principle.
Redshift and Hubble's law
Atoms give out light at fixed wavelengths (spectral lines). In light from distant galaxies these lines appear at longer wavelengths, shifted towards red. This is redshift:
z = Δλ / λ₀, and for speeds much less than light, z ≈ v / c.
In 1929 Edwin Hubble (building on work by Vesto Slipher, Henrietta Leavitt and Georges Lemaître) found that the farther a galaxy is, the bigger its redshift. This is Hubble's law:
v = H₀ d
H₀ is the Hubble constant, about 70 km s⁻¹ Mpc⁻¹: for every megaparsec of distance, a galaxy recedes about 70 km/s faster. (Different methods give values from about 67 to 73; scientists are still working out why.)
The best explanation is that space itself is expanding. Galaxies are not flying through space from one centre; the space between them grows, like dots on an inflating balloon. Light travelling through that space is stretched too, which is the cosmological redshift. Nearby galaxies (like Andromeda) can still move towards us because gravity wins over short distances.
The Big Bang and its evidence
If everything is moving apart now, it was closer in the past. Going back far enough, the universe was extremely hot and dense. The expansion from that state is the Big Bang. It was not an explosion at one point in space; it happened everywhere at once.
Age estimate: if galaxies always moved at the same speed, the time since they were together is t = d / v = 1 / H₀. With H₀ = 70 km s⁻¹ Mpc⁻¹ this gives about 14 billion years. Careful modern measurements give 13.8 billion years.
Three main pieces of evidence:
- Redshift of galaxies (Hubble's law): the universe is expanding.
- Cosmic microwave background (CMB): found in 1965 by Penzias and Wilson. It is faint microwave radiation from every direction, matching a black body at about 2.7 K. It is light released about 380 000 years after the Big Bang, when the universe cooled enough for atoms to form, then stretched by expansion into microwaves. Its tiny ripples were the seeds of today's galaxies.
- Light elements: the first few minutes were hot enough for nuclear fusion, making about 75% hydrogen and 25% helium by mass, just what we observe in the oldest stars and gas clouds.
Short timeline: Big Bang → first seconds: particles form → about 3 minutes: hydrogen and helium nuclei → about 380 000 years: atoms, CMB released → a few hundred million years: first stars and galaxies → 9.2 billion years: Sun and Earth form → today.
Dark matter, dark energy and the fate of the universe
Dark matter: stars at the edge of galaxies orbit much faster than the visible matter's gravity allows (flat rotation curves). Clusters also bend light (gravitational lensing) more than their visible mass can. So there must be extra, invisible mass that does not give out light. We still do not know what it is.
Dark energy: in 1998, studies of distant Type Ia supernovae (exploding stars of known brightness) showed that the expansion is speeding up. Whatever causes this is called dark energy.
Recipe of the universe today (approximately): ordinary matter 5%, dark matter 27%, dark energy 68%.
Black holes are regions where gravity is so strong that nothing, not even light, can escape. Supermassive black holes, millions to billions of times the Sun's mass, sit at the centres of most large galaxies, including ours.
The future depends on the balance between gravity and dark energy. With dark energy as measured, the universe will probably keep expanding forever, growing colder and darker (the 'big freeze').
Key formulas and definitions
- Redshift: z = Δλ / λ₀ = (λ_observed − λ₀) / λ₀
- For v ≪ c: z ≈ v / c (c = 3.00 × 10⁵ km/s)
- Hubble's law: v = H₀ d, H₀ ≈ 70 km s⁻¹ Mpc⁻¹
- Hubble time (age estimate): t ≈ 1 / H₀ ≈ 977.8 / H₀ billion years (H₀ in km s⁻¹ Mpc⁻¹)
- 1 pc = 3.26 ly = 3.09 × 10¹⁶ m; 1 Mpc = 3.09 × 10²² m
- Wien's law for the CMB: λ_max = 2.9 × 10⁻³ m K / T
Worked examples
1. A galaxy is 200 Mpc away. Using H₀ = 70 km s⁻¹ Mpc⁻¹, how fast is it receding?
v = H₀ d = 70 × 200 = 14 000 km/s.
2. A galaxy recedes at 7 000 km/s. How far away is it (H₀ = 70 km s⁻¹ Mpc⁻¹)?
d = v / H₀ = 7 000 / 70 = 100 Mpc.
3. A hydrogen line normally at 656.3 nm is seen at 669.4 nm. Find z and the recession speed.
Δλ = 669.4 − 656.3 = 13.1 nm. z = 13.1 / 656.3 ≈ 0.020. v ≈ z c = 0.020 × 3.00 × 10⁵ ≈ 6 000 km/s.
4. Estimate the age of the universe from H₀ = 70 km s⁻¹ Mpc⁻¹.
Convert: 1 Mpc = 3.09 × 10¹⁹ km. H₀ = 70 / 3.09 × 10¹⁹ = 2.27 × 10⁻¹⁸ s⁻¹. t = 1 / H₀ = 4.4 × 10¹⁷ s. Divide by 3.16 × 10⁷ s per year: about 1.4 × 10¹⁰ years = 14 billion years.
5. The CMB has a temperature of 2.7 K. At what wavelength is it brightest?
λ_max = 2.9 × 10⁻³ / 2.7 ≈ 1.1 × 10⁻³ m ≈ 1.1 mm: microwaves.
6. If H₀ were 50 km s⁻¹ Mpc⁻¹ instead of 70, would the estimated age be larger or smaller? By how much?
t ≈ 977.8 / H₀. For 50: about 19.6 billion years; for 70: about 14.0 billion years. A smaller H₀ means slower expansion, so a larger age (about 5.6 billion years more).
Common mistakes
- Picturing the Big Bang as an explosion from one point into empty space. Space itself expanded, everywhere at once.
- Thinking we are at the centre because everything moves away from us. Every galaxy sees the same thing; there is no centre.
- Forgetting units in Hubble's law. With H₀ in km s⁻¹ Mpc⁻¹, put d in Mpc to get v in km/s; convert Mpc to km for the age.
- Using z ≈ v/c for very large redshifts. It only works well when v is much smaller than c (z below about 0.1).