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The first minutes and the light elements

How temperature and expansion speed set helium and deuterium

Sandbox Physics ·

About a quarter of the ordinary matter in the universe is helium, and roughly one hydrogen atom in forty thousand is deuterium. Both numbers were fixed within the first few minutes after the big bang. Temperature decided when atomic nuclei could hold together; the speed of the expansion decided how long the universe took to get there, and therefore how many neutrons were still around to build them.

A hot soup that keeps changing its mind

One second after the big bang the universe was at about ten billion kelvin. It held light, electrons and their antimatter partners the positrons, neutrinos, and a thin sprinkling of protons and neutrons, the two particles that make up atomic nuclei. There were more than a billion particles of light for every proton or neutron.

In that soup protons and neutrons kept turning into each other. A neutron hit by a positron became a proton; a proton hit by an electron became a neutron. These changes run on the weak nuclear force. A neutron is slightly heavier than a proton, so making one costs a little energy. While the soup was very hot that cost hardly mattered and the two were almost equally common. As it cooled, the cheaper particle, the proton, began to win.

The first clock: neutrons stop being made

The weak reactions slow down very quickly as the temperature drops, much faster than the expansion itself slows. Within the first two seconds they fell behind: the soup was thinning out faster than collisions could keep converting particles. From then on the share of neutrons stopped following the temperature. By about ten seconds there was roughly one neutron for every five protons.

That was not the end of the neutrons' troubles. A free neutron is unstable. On its own it decays into a proton, an electron and an antineutrino, with an average lifetime of about fifteen minutes. The neutrons left over from the first seconds were on a timer.

The second clock: deuterium falls apart

The way out for a neutron is to join a nucleus, where it is protected from decay. The first step is deuterium, a proton and a neutron stuck together. Pulling that pair apart takes 2.2 million electronvolts, a small amount by nuclear standards.

At ten seconds the average particle of light already carried much less energy than that. It did not help. Light outnumbered protons and neutrons by more than a billion to one, and a tiny fraction of it always carries far more energy than the average. With so many particles of light, that fraction was still enough to break every new deuterium nucleus almost as soon as it formed. Physicists call this the deuterium bottleneck.

The bottleneck opened only when the temperature fell to about 800 million kelvin, roughly four minutes after the big bang. By then decay had removed a further fraction of the neutrons, leaving about one for every seven protons.

Almost every surviving neutron becomes helium

Once deuterium survives, a quick chain of collisions turns it into helium-4, two protons and two neutrons bound tightly together. Within a minute or so nearly every remaining neutron ends up there.

That gives a simple count. Take sixteen particles with one neutron for every seven protons: two neutrons and fourteen protons. The two neutrons grab two protons and form one helium nucleus, leaving twelve protons as hydrogen. Helium then carries four of the sixteen units of mass, or 25 percent. Careful calculations, which follow every reaction and the exact timing, give 24.7 percent. The simplified network in the companion Lab gives 24.2 percent.

Astronomers measure the helium share in the gas of small galaxies that have formed very few stars. The current best value is 24.5 percent with an uncertainty of 0.3 percent, as summarised in the 2025 Review of Particle Physics.

Why the expansion speed matters

The expansion rate in those minutes was set by the energy of everything that moved close to the speed of light: light itself, electrons and positrons, and three kinds of neutrinos. More of that energy means faster expansion.

Faster expansion raises the helium in two ways. The weak reactions fall behind earlier, while the soup is hotter and neutrons are more common. And the wait for the deuterium bottleneck is shorter, so fewer neutrons decay. An extra kind of light particle, as energetic as one more neutrino, would add about 1.3 percentage points of helium. The measured helium leaves room for much less than that. Combined with deuterium, it gives an effective number of neutrino types of 2.90 with an uncertainty of 0.14, in line with the three that particle physics knows.

Deuterium is the leftover fuel

Deuterium is not an end product. Most of it is burned into helium-3 and helium-4 in the minutes after the bottleneck opens. The more protons and neutrons are packed into each volume, the more often deuterium nuclei meet and burn, and the less deuterium is left. So the deuterium that survives measures how much ordinary matter the universe contains.

The cleanest measurements come from distant gas clouds that are seen in silhouette against even more distant quasars. They give about 2.5 deuterium atoms for every hundred thousand hydrogen atoms, which corresponds to about six protons and neutrons for every ten billion particles of light. The cosmic microwave background, the light released 380,000 years later, gives the same density through entirely different physics. This agreement is one of the strongest checks that the hot big bang picture is right.

One element does not fit

The same calculation predicts how much lithium-7 should have been made. The oldest stars in our galaxy show about three times less. Neither better nuclear measurements nor the precise deuterium value has removed the gap. The review cited above, and the detailed study by Fields and colleagues, describe it as unresolved. The leading explanation is that stars slowly destroyed part of their own lithium, while new physics in the first minutes remains an open possibility.

Try it in the Lab

Play Our universe and drag the cosmic clock through the moment helium appears. Open the light-element network Lab

Next: When neutrons and protons stop turning into each other

Sources

  1. 2025 Review of Particle Physics
  2. Fields and colleagues

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What this page links to directly

The first minutes and the light elements · Reading path

From the first second to the light elements

  1. You are hereHow temperature and expansion speed set helium and deuterium
  2. ArticleWhen neutrons and protons stop turning into each other
  3. ArticleWhy deuterium waits for the universe to cool
  4. ArticleHow baryon density and extra radiation move the light elements
  5. ArticleRecompute a small network from a frozen rate grid and propagate rate errors
  6. ArticleReading the BBN evidence on extra radiation and the lithium problem
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