Cosmology: Redshift, Hubble's Law and the Big Bang

The Expanding Universe

One of the most profound discoveries in science is that the universe is expanding. In the 1920s, astronomers began measuring the spectra of distant galaxies and noticed something remarkable: the absorption lines in almost every galaxy’s spectrum were shifted to longer, redder wavelengths. This redshift indicates that galaxies are moving away from us. The more distant a galaxy, the greater its redshift — and therefore the faster it is receding. This is not galaxies moving through space; it is space itself that is expanding, carrying galaxies apart like raisins in a rising dough.

The Redshift Formula

The relationship between observed wavelength shift and recession velocity is given by:

$$\frac{\Delta\lambda}{\lambda} = \frac{v}{c}$$

where \(\Delta\lambda\) is the change in wavelength (observed minus rest wavelength), \(\lambda\) is the rest wavelength, \(v\) is the recession velocity of the galaxy, and \(c\) is the speed of light (3 × 10⁸ m/s). A galaxy with \(\Delta\lambda / \lambda = 0.05\) is receding at 5% of the speed of light. This formula applies for velocities much less than \(c\); at very high redshifts (quasars, early universe), relativistic corrections are needed.

Hubble’s Law

In 1929, Edwin Hubble published his finding that galaxy recession velocity is proportional to distance:

$$v = H_0 d$$

where \(v\) is the recession velocity in km/s, \(d\) is the distance in megaparsecs (Mpc), and \(H_0\) is the Hubble constant \(H_0 \approx 70\) km/s/Mpc. This means that a galaxy 100 Mpc away is receding at approximately 7,000 km/s. Hubble’s law implies that the universe had a beginning: running the expansion backwards gives an age for the universe of approximately \(1/H_0 \approx 13.8\) billion years. This is consistent with the independently measured ages of the oldest stars.

The Big Bang Theory — Evidence

The Big Bang theory proposes that the universe began in an extremely hot, dense state approximately 13.8 billion years ago and has been expanding and cooling ever since. Three key pieces of observational evidence support it:

• Hubble’s law and galaxy redshifts — all galaxies (except local group members bound by gravity) are receding; the farther away, the faster. Running the expansion backwards implies a single origin point.
• The cosmic microwave background (CMB) — in 1965, Arno Penzias and Robert Wilson discovered a faint, uniform cosmic microwave background radiation coming equally from all directions. Its temperature is approximately 2.7 K — the predicted cooled remnant of the hot early universe. The CMB could not have a competing explanation as a Steady State relic. Tiny temperature fluctuations (anisotropies) in the CMB, mapped by WMAP and the Planck satellite, reveal the seeds of the large-scale structure that grew into today’s galaxies.
• Quasar distribution — quasars are found predominantly at high redshifts (great distances, early cosmic time). This shows the universe was different in the past — inconsistent with the Steady State model, which requires the universe to look the same at all epochs.

The Steady State theory, championed by Fred Hoyle, predicted that the universe would look the same at all epochs, with matter being continuously created to fill in the expanding gaps. The discovery of the CMB and the distribution of quasars decisively rejected this model.

Dark Matter

Observations of galactic rotation curves show that stars far from the galactic centre orbit much faster than the visible mass of the galaxy can account for. If only visible matter were present, orbital speeds should decrease with distance (like planets in the Solar System). Instead, they remain roughly constant — implying a large amount of unseen mass, called dark matter, distributed throughout the galactic halo. Dark matter cannot be detected electromagnetically: it does not emit, absorb or reflect light. Its nature remains unknown; candidates include weakly interacting massive particles (WIMPs) and axions. Dark matter accounts for approximately 27% of the total energy density of the universe.

Dark Energy and the Fate of the Universe

In 1998, observations of Type Ia supernovae at great distances showed that the universe’s expansion is accelerating — not slowing as gravity should cause. This acceleration is attributed to dark energy — a form of energy intrinsic to space itself, accounting for about 68% of the universe’s total energy content. Dark energy is even more poorly understood than dark matter; it cannot currently be detected directly.

The future of the universe depends on the relative strengths of gravity (trying to decelerate expansion) and dark energy (trying to accelerate it). Current models suggest three possible fates:

• Big Freeze (most likely in current models): expansion continues indefinitely; galaxies drift apart; stars use up their fuel; the universe cools towards absolute zero.
• Big Crunch: gravity eventually overcomes expansion and the universe collapses back to a singularity (requires dark energy to weaken).
• Big Rip: dark energy strengthens over time, eventually ripping apart all structures — galaxies, then stars, then atoms — as the expansion rate becomes infinite.