You already know the great clue: the light from almost every galaxy is red-shifted, so almost every galaxy is racing away from us, and the whole Universe is expanding. Cosmology is the science that takes that single clue seriously and pushes it as far as it will go — backwards, to ask how the Universe began, and forwards, to ask how it will end.

The whole story hangs off one deceptively simple straight-line graph that Edwin Hubble drew in 1929. Measure how fast a galaxy is receding, and measure how far away it is, and you find they are in lockstep: twice as far means twice as fast. That proportionality — Hubble's law — is the beating heart of this page. From it we will read off the age of the Universe, meet the evidence that pins down the Big Bang, and weigh up the invisible dark matter and dark energy that will decide the Universe's fate.

Hubble's law: further means faster, in exact proportion

For every galaxy, Hubble compared two numbers: its recession velocity v (how fast it moves away, read off its red-shift as v \approx cz) and its distance d. Plotted against each other, the points fall on a straight line through the origin. In symbols,

where the constant of proportionality H_0 is the Hubble constant — the same for every galaxy in the sky. Because the graph is a straight line through the origin, H_0 is simply its gradient: H_0 = v/d. Its usual units make this obvious — kilometres per second of recession, per megaparsec of distance:

Read that as: "for every megaparsec (about 3.1\times10^{19}\ \text{km}) further out you look, galaxies recede about 70\ \text{km/s} faster." There is nothing special about us here — as you saw with the raisin-bread model, an observer in any galaxy sees exactly the same law, because it is space itself that is stretching, carrying every galaxy away from every other.

See the law for yourself

Below is the velocity–distance graph. The straight line through the origin is Hubble's law: its gradient is the Hubble constant. Drag the H₀ slider and watch the whole line pivot — a bigger Hubble constant is a steeper line, so galaxies at a given distance recede faster. Then drag the distance slider to slide the marker along the line and read off the recession velocity v = H_0 d for a galaxy that far away.

Worked example: recession velocity

A galaxy is measured to be d = 250\ \text{Mpc} away. Taking H_0 = 70\ \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}, how fast is it receding?

Step 1 — write down Hubble's law.

Step 2 — substitute (the Mpc cancel neatly).

So the galaxy is rushing away at about 1.75\times10^{4}\ \text{km/s} — roughly 6\% of the speed of light. Its red-shift would be about z \approx v/c \approx 0.058.

Worked example: the age of the Universe from 1/H₀

Here is Hubble's law's most spectacular payoff. If every galaxy has been receding at a steady speed v ever since the Big Bang, then the time it has taken to reach its current distance d is just distance over speed, t = d/v. But Hubble's law says v = H_0 d, so

The distance cancels — every galaxy gives the same answer. That single number 1/H_0 is an estimate of the age of the Universe. To get it in seconds we must feed H_0 in SI units, so first convert away the kilometres and megaparsecs.

Step 1 — convert H_0 to per-second. Use 1\ \text{Mpc} = 3.09\times10^{19}\ \text{km}:

Step 2 — take the reciprocal.

Step 3 — turn seconds into years (one year \approx 3.16\times10^{7}\ \text{s}):

Astonishingly close to the modern figure of 13.8 billion years — from nothing but the gradient of a graph. (The small discrepancy is expected: the expansion has not been perfectly steady, which is exactly the twist we come to at the end.)

The evidence for the Big Bang

Hubble's law tells us the Universe is expanding today. Rewind that expansion and everything crowds together into a hot, dense beginning about 13.8 billion years ago — the Big Bang. But a good scientific theory must make testable predictions, and the Big Bang model rests on three great pillars of evidence:

• The red-shift of galaxies. The uniform Hubble expansion itself — every distant galaxy receding, the further ones faster — is precisely what a Universe growing from a single hot point should look like.
• The cosmic microwave background (CMB). If the early Universe was blazingly hot, it should have been filled with radiation that still bathes the whole sky today — cooled and stretched by 13.8 billion years of expansion from searing visible light down to feeble microwaves. This afterglow was found in 1965, glowing at the same 2.7\ \text{K} from every direction. It is the single most powerful confirmation of the Big Bang.
• The abundance of the light elements. In its first few minutes the whole Universe was hot enough for nuclear fusion, forging hydrogen into helium. The Big Bang model predicts the Universe should be about 75\% hydrogen and 25\% helium (with a trace of lithium) — and that is exactly the ratio we measure in the oldest, most pristine gas.

Three independent lines of evidence, all pointing the same way. That is why the Big Bang is no longer "a theory" in the everyday sense but the accepted history of our Universe.

The fate of the Universe: a tug-of-war

Now look forwards. The Universe is expanding — but every scrap of matter in it pulls on every other scrap through gravity, trying to brake that expansion. The Universe's fate is a tug-of-war between the outward expansion and inward gravity, and the winner is decided by one number: how much mass and energy is packed into each cubic metre — the Universe's average density \rho, compared with a special critical density \rho_c.

Ignoring the twist to come, the simple gravitational picture gives three possible futures:

• Too dense (\rho > \rho_c) — a "closed" Universe. Gravity wins: the expansion slows, halts, and reverses into a collapse — everything crashing back together in a Big Crunch.
• Too sparse (\rho < \rho_c) — an "open" Universe. Gravity loses: the Universe expands forever, galaxies drifting apart without limit.
• Exactly critical (\rho = \rho_c) — a "flat" Universe. The knife-edge case: expansion slows towards zero but never quite stops.

So to predict the end of the Universe, cosmologists must weigh it — add up all the mass and energy it contains. And when they did, they got two enormous surprises.

The two surprises: dark matter and dark energy

Surprise one — dark matter. Weigh a galaxy by its starlight and it comes out far too light to explain its own motion. Stars at the edge of a spinning galaxy orbit far too fast — gravity from the visible stars alone could never hold them in; they should fly off. Something unseen must be supplying the extra pull. We call it dark matter: matter that has mass and gravity but gives off no light. It outweighs all the ordinary stars and gas by roughly five to one.

Surprise two — dark energy. In 1998, astronomers measured the expansion in the distant past (using exploding stars as standard beacons) expecting to see gravity gradually slowing it down. Instead they found the opposite: the expansion is speeding up. Some mysterious dark energy — an energy of empty space itself — pushes outward and is winning the tug-of-war, driving an accelerating expansion.

Add it all up and the Universe's energy budget is dominated by the things we cannot see: roughly 68% dark energy, 27% dark matter, and only about 5% ordinary matter — every star, planet, and person combined. Because dark energy dominates and drives acceleration, current evidence points not to a Big Crunch but to an endless, ever-faster expansion: galaxies thinning out, stars burning out, the Universe growing cold, dark and empty. Cosmologists call this most likely fate the Big Freeze (or "Heat Death").