The universe is expanding: distant galaxies are flying apart, and the space between them is stretching. Now do the boldest thing a physicist can do with an expanding thing — run the film backwards. As you wind the clock back, everything rushes together, the density climbs, and, crucially, the temperature soars. Squeeze any gas and it heats up; the whole cosmos is no exception. Wind back far enough and there are no galaxies, no stars, not even atoms — just a searing, uniform plasma of nuclei, electrons and light, hotter than the centre of the Sun and filling all of space. That is the hot Big Bang.

And here is the astonishing part: we can still see it. The oldest light in existence is reaching us right now, from every direction in the sky, a faint microwave glow left over from when that fireball finally cooled enough to become transparent. It is called the cosmic microwave background (CMB), and it is the single strongest piece of evidence that the universe really did begin hot and dense. This page follows the cooling universe through its first few hundred thousand years — the forging of the first atomic nuclei, and the moment the fog cleared and released the light we still bathe in today.

Cooling as it expands: temperature and redshift

The engine behind the whole story is one simple scaling law. Let a(t) be the cosmic scale factor — a number that tracks how much space has stretched, set to a = 1 today and smaller in the past. As the universe expands, the wavelength of every photon is stretched along with space, so its energy drops and the radiation cools. Carefully done, the blackbody temperature of the cosmic radiation obeys

where z is the redshift — the same redshift we measure for distant galaxies, now applied to the primordial light itself. Small a (the deep past) means large 1+z and therefore an enormous temperature. Written with the temperature we measure today, T_0, this is the master equation of the early universe:

This single law lets us read the universe's history like a temperature ladder. From hot to cold: a soup of quarks and gluons, then protons and neutrons freezing out of that soup, then the first atomic nuclei (nucleosynthesis), then — much later and much cooler — the first neutral atoms (recombination), which is where our light comes from. Two of these rungs are the heart of this page.

The first three minutes: Big Bang nucleosynthesis

Roll back to about one second after the beginning. The temperature is around 10^{10}\ \text{K}, and the universe is a dense broth of protons, neutrons, electrons, neutrinos and photons, all colliding furiously. Neutrons and protons interconvert until, as things cool, the reactions can no longer keep up and the neutron-to-proton ratio freezes out at roughly n/p \approx 1/7 (neutrons are slightly heavier, so they are slightly rarer).

You might expect the protons and neutrons to fuse into helium immediately — but they can't yet. The first step is to build deuterium (a proton + a neutron), and at these temperatures any deuterium is instantly blasted apart by the fierce bath of photons. This deuterium bottleneck holds up the whole assembly line until the universe cools below the deuterium binding energy, at about T \approx 10^{9}\ \text{K} — reached only a few minutes in. Then the floodgates open: deuterium survives, and in a brief burst nearly every available neutron is swept up into the tightly bound nucleus {}^{4}\text{He}.

The result, set almost entirely by that frozen n/p ratio, is a universe of ordinary matter that is about 75% hydrogen and 25% helium-4 by mass, with a whisper of leftover deuterium, {}^{3}\text{He} and {}^{7}\text{Li}. Everything heavier — the carbon in you, the oxygen you breathe, the iron in your blood — had to wait hundreds of millions of years to be cooked inside stars. Big Bang nucleosynthesis makes the light stuff; stars make the rest.

The measured light-element abundances agree with the theory across many orders of magnitude, and — because how much of each element you make depends on how many baryons there were to make it from — they pin down the baryon density of the universe. That the observed cosmic helium fraction sits right at the predicted 25% is one of the great quantitative triumphs of the hot Big Bang picture.

Recombination: the fog clears

Now let the universe keep expanding and cooling for a few hundred thousand years. For all that time it stays an opaque plasma: the electrons are still free, not bound into atoms, and free electrons are ferociously good at scattering light. A photon can travel barely any distance before it ricochets off an electron and heads off in a random direction. Light is trapped, bouncing endlessly — the universe glows like the inside of the Sun, brilliant but foggy, and you could not see across it.

Then, at about 380,000 years, the temperature drops to roughly T \approx 3000\ \text{K} (redshift z \approx 1100). This is cool enough that electrons can finally stick to protons and stay stuck, forming neutral hydrogen atoms. This event is called recombination. The moment the electrons vanish into atoms, there is almost nothing left to scatter the photons — and the fog instantly clears. The universe becomes transparent, and the photons, freed at last, stream in straight lines across the cosmos. This release is called decoupling, or the last scattering of the photons.

Every photon of the CMB last touched matter at that surface and has been travelling straight to us ever since. Look far enough in any direction and you are looking back to z \approx 1100 — to the wall of the fireball, the oldest thing it is possible to see.

The whole history on one line

Because T = T_0(1+z) is exactly proportional, the universe's temperature history is a perfectly straight line through the origin: the further back you look (larger 1+z), the hotter it was, in strict proportion. Drag the slider to wind the clock back and read off the temperature at any redshift. Two rungs of the ladder are marked: the cool today near the origin, and hot recombination at z \approx 1100 where the CMB is born. (Nucleosynthesis lies far off the right-hand edge, at z \sim 10^{8} and billions of kelvin.)

The CMB today: a redshifted fireball

Those photons set free at 3000\ \text{K} have been travelling for 13.8 billion years, and all that time space has been stretching underneath them. By the master law their temperature has fallen by the same factor the universe has grown — about 1100 — cooling their blackbody spectrum from a glowing 3000\ \text{K} down to a frigid

just a few degrees above absolute zero. A blackbody that cold peaks in the microwave band, at a wavelength of about a millimetre — which is exactly where we find it. The CMB is one of the most perfect blackbody spectra ever measured, anywhere.

Its existence was predicted by Ralph Alpher and George Gamow in the late 1940s as a leftover glow from the hot Big Bang, and then discovered by accident in 1965 by Arno Penzias and Robert Wilson, who found an inexplicable hiss in their radio antenna coming equally from every direction. The glow is astonishingly uniform — the same temperature to a few parts in a hundred thousand all over the sky — but not perfectly so. Superimposed on the smooth 2.725\ \text{K} are faint ripples,

tiny hot and cold patches that map the density variations of the infant universe. Those over-dense patches are the seeds of all structure: gravity spent the next billions of years amplifying them into the galaxies, clusters and cosmic web we live in. The precise pattern of these ripples — the acoustic peaks, measured ever more sharply by COBE, WMAP and Planck — encodes the geometry and contents of the cosmos, telling us that space is flat and that ordinary matter is outweighed by dark matter and dark energy.

Worked examples

Example 1 — the redshift of last scattering. The CMB photons were emitted when the universe was at T_\text{emit} \approx 3000\ \text{K}, and we receive them at T_0 = 2.725\ \text{K}. By how much have they been redshifted? Rearrange the master law T = T_0(1+z):

The wavelength of every CMB photon has been stretched by a factor of about 1100 on its journey to us — a direct measure of how much the universe has expanded since it was 380,000 years old.

Example 2 — where the spectrum peaks (Wien's law). A blackbody at temperature T radiates most strongly at a wavelength given by Wien's displacement law, \lambda_\text{peak} = \dfrac{2.898\times 10^{-3}\ \text{m·K}}{T}. For the CMB at T_0 = 2.725\ \text{K}:

About a millimetre — squarely in the microwave. (Back at 3000\ \text{K} the same law gives \lambda_\text{peak} \approx 966\ \text{nm}, in the near-infrared — the fireball glowed a dull red-white. The expansion has since stretched that peak by the same factor \sim 1100, exactly as it should.)

Example 3 — the primordial helium fraction. Almost every neutron that survived freeze-out ends up inside a {}^{4}\text{He} nucleus, which holds two protons and two neutrons. If the neutron-to-proton ratio is r = n/p \approx 1/7, the fraction of the ordinary-matter mass locked up as helium is

A quarter of the ordinary matter, by mass, comes out as helium — and that is exactly the primordial abundance astronomers measure in the oldest, most pristine gas clouds. A ratio frozen in during the first second predicts the chemical make-up of the entire universe.