The Expanding Universe

Core idea

The universe is not static. In 1929 Hubble noticed that the light from distant galaxies is systematically redshifted by amounts proportional to their distances — they are receding, and the farther they are, the faster they go. The implication is geometric: space itself is expanding, and if you run the film backward everything was once concentrated at a single point of infinite density. General relativity predicts that this initial singularity is unavoidable given the matter we observe, and that the theory itself breaks down there.

Hawking's argument: With Roger Penrose I showed in 1970 that, given general relativity is correct and the universe contains as much matter as we measure, time must have had a beginning at a big bang singularity. The price is that the theory cannot describe its own starting condition — quantum effects must take over.

Why it matters

Hubble's measurement and the Doppler shift

Light from a source moving toward us is blueshifted (compressed wavelengths); light from a source moving away is redshifted (stretched). When astronomers in the 1920s catalogued the spectra of distant galaxies, the absorption lines that should sit at specific colours were all shifted toward the red — and the size of the shift was proportional to the galaxy's distance. The cosmos is not a randomly milling crowd; it is a coherent recession. The simplest interpretation, taken seriously only by the Russian mathematician Alexander Friedmann, is that space itself stretches and carries the galaxies apart.

Friedmann's three universes

Friedmann assumed only two things: the universe looks the same in every direction, and it would look that way from anywhere. From this cosmological principle he derived three families of solutions. Either the universe expands and recollapses (positive curvature, finite space), expands forever at a steady speed (negative curvature, infinite space), or expands at exactly the critical rate that asymptotically approaches but never reaches zero (flat space). Which one we live in depends on the actual matter density. Visible matter accounts for under 1% of the critical density; dark matter raises this to roughly 10%; the remainder is the open question.

The cosmic microwave background

In 1965 Penzias and Wilson, debugging a microwave antenna at Bell Labs, kept hearing a uniform hiss they could not eliminate. Dicke and Peebles at Princeton, working on a hypothesis of George Gamow's, had predicted exactly this: a glow from the hot early universe, redshifted by cosmic expansion into the microwave band. The signal is the same in every direction to one part in 100,000, confirming Friedmann's first assumption with extraordinary precision. The tiny variations COBE measured in 1992 are the seeds of every galaxy.

The singularity theorems

Lifshitz and Khalatnikov initially argued that singularities were peculiar artefacts of Friedmann's idealised models. Penrose's 1965 theorem showed otherwise for collapsing stars; Hawking adapted the argument by reversing time, proving that any expanding Friedmann-like universe must have begun in a singularity. By 1970, the joint Penrose–Hawking theorems established that the big bang is a necessary consequence of general relativity plus the observed matter content. The same theorems also indicate that general relativity predicts its own failure: at the singularity the curvature is infinite and the theory cannot tell us what happened.

Key takeaways

Mental model

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Practical application

A practical reading habit: when a cosmology article quotes a "Hubble tension," it is reporting the present-day difference between two independent ways to measure the expansion rate — one from the CMB, one from supernovae. The fact that the two methods disagree at the 5σ level is a real puzzle. If the discrepancy survives further scrutiny it signals that the cosmological model needs revision; if it goes away it will be because a measurement bias was eventually identified. Either outcome confirms Hawking's general point — every theory in cosmology is provisional.

Example

Look at the spectrum of a quasar at redshift z ≈ 6. The hydrogen Lyman-α emission line, intrinsically at 121.6 nm in the ultraviolet, has been stretched to 851 nm in the near-infrared by the time it reaches an Earth telescope — a factor of seven elongation. That's not the quasar moving through space at near-light speed in the conventional Doppler sense; the cosmological redshift measures how much space itself has expanded during the photon's journey. The universe was one-seventh its present size when that light was emitted, roughly a billion years after the big bang.

A more domestic example of the same physics: take any galaxy in the SDSS catalogue, look up its redshift, multiply by the speed of light, divide by Hubble's constant (about 70 km/s/Mpc). You get the galaxy's distance. The fact that this procedure works — that one number, the redshift, encodes both motion and distance for objects we cannot otherwise reach — is the operational meaning of "the universe is expanding."

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