The first minutes and the oldest light

The universe began hot. One second after the start, everything was a soup of light and tiny particles at ten billion degrees.

As space spread out, the soup cooled. Over the next few minutes some of the particles stuck together, and that made the two lightest elements, hydrogen and helium. Nearly all the hydrogen in the universe today, and most of the helium, dates from then. The hydrogen in the water you drink is that old.

For a long time after that, the universe was a glowing fog. Light could not get anywhere, because it kept bumping into loose particles. Then, about 380,000 years after the start, it cooled enough for the first whole atoms to form. The fog cleared, and light could travel freely for the first time.

That light has been travelling ever since, and it is still arriving, from every part of the sky. It is far too faint and stretched out to see with your eyes, but radio telescopes pick it up. It is the oldest light there is, a picture of the universe when it was very young.

The order of events. These are the stages of the early universe as cosmologists now understand them. The times are counted from the start of the expansion.

When	What happened
The first second	Quarks joined in threes to make protons and neutrons. Matter and antimatter wiped each other out, leaving a small surplus of matter.
One second	A soup of light and particles at about 10 billion degrees.
The first few minutes	Protons and neutrons fused into the nuclei of helium, with traces of other light elements.
380,000 years	The first whole atoms formed, the fog cleared, and the oldest light was set free.
The next 200 million years	No stars yet. This stretch is called the dark ages.
After that	The first stars lit, and over several hundred million years gathered into the first galaxies.

Making the elements. A proton on its own is the nucleus of a hydrogen atom, so the hydrogen was there from the first second. For a few minutes the whole universe was also hot and dense enough for nuclear fusion, the process that powers the Sun. Protons and neutrons joined, and nearly every neutron ended up inside a helium nucleus, which has two protons and two neutrons.

How much helium this makes comes down to counting. When the fusion began there was about one neutron for every seven protons. Take sixteen particles: two neutrons and fourteen protons. The two neutrons and two of the protons make one helium nucleus. Twelve protons are left over as hydrogen. Four of the sixteen particles are in helium, which is a quarter.

So the theory says a quarter of the ordinary matter that came out of the first minutes was helium, by mass, and nearly all the rest was hydrogen. The helium measured in gas that has hardly been touched by stars since then is 24.5 per cent.

Fusion also left small traces: about 25 atoms of heavy hydrogen, called deuterium, for every million of the ordinary kind, and far less lithium. Then it stopped. After about five minutes the universe had thinned and cooled too much for nuclei to go on joining. There was no carbon, no oxygen and no iron. Every heavier element came much later, from stars.

The fog. For the next 380,000 years the universe was a plasma, a hot gas of bare nuclei and loose electrons. Light cannot cross a plasma like that. It hits an electron, bounces off in a new direction, and hits another. The universe glowed, but it was opaque.

The clearing. By about 380,000 years the temperature had dropped to about 3,000 K. Electrons could now settle onto nuclei and stay there, making the first complete atoms. Cosmologists call this recombination. With the loose electrons gone, light had nothing to bounce off, and it set out in straight lines.

That light is the cosmic microwave background. When it set out it was the glow of a gas at 3,000 K. The expansion of space has since stretched its waves to about a millimetre long, which makes it microwaves, and its temperature today is 2.7 K, about −270 °C. Every cubic centimetre of space holds about 400 particles of this light.

How it was found. In the late 1940s George Gamow, Ralph Alpher and Robert Herman were working on how the first elements were made. They saw that a universe hot enough to make them would have left a glow behind, and that by now it should have cooled to no more than about 5 degrees above absolute zero.

In 1964 Arno Penzias and Robert Wilson were using a radio antenna at Bell Laboratories in New Jersey, built for talking to early satellites. It picked up more microwaves than it should. They thought the fault was in the antenna or the air, and tested everything. The signal stayed, and it was the same in every direction. It was coming from the whole sky. They were given a Nobel Prize for it in 1978.

What it shows. The COBE satellite, launched in 1989, measured the glow across many wavelengths. The first result, after nine minutes of observing, was a perfect blackbody curve, the kind of light given out by something at one single temperature. The Big Bang is the only account of the universe that predicts a glow like that.

COBE also found that the glow is not quite even. Some patches of sky are warmer or cooler than others by about one part in 100,000. These mark places where the young universe was very slightly denser or thinner. Gravity pulled more matter into the denser places, and over billions of years they grew into galaxies and clusters of galaxies. The cosmic web began as these faint marks.

Two later spacecraft, NASA’s WMAP and the European Planck, mapped the patches in much finer detail. The pattern gives the age of the universe, 13.8 billion years, and what it is made of: ordinary matter is only 4.9 per cent.

The dark ages. After the oldest light was released there was nothing new to shine. The universe was hydrogen and helium gas, slowly gathering under gravity. It took about 200 million years for the first stars to light. They are thought to have been 30 to 300 times the mass of the Sun.

Still being worked out. The amount of lithium predicted for the first minutes is about three times what is found in the oldest stars. It may be that stars destroy some of their lithium, or it may be that something is missing from the theory.

What the 3D view shows. Pull back as far as the view goes and a mottled sphere closes round everything. It is a real map of the oldest light, made by the WMAP spacecraft, and it is drawn 46 billion light years away, where the matter that sent the light is now. The colours stand for the warmer and cooler patches, with the differences made enormously stronger so they can be seen. In truth the glow is even to one part in 100,000. The sphere is not a wall. It is the furthest we can see, because beyond it we would be looking into the fog.

Temperature as energy. Particle physicists give the temperature of the early universe as an energy, the typical energy of one particle. One electron volt corresponds to 11,605 K, so a temperature of 1 MeV, a million electron volts, is 11.6 billion kelvin. The universe was at about 1 MeV when it was about one second old.

Neutrons and protons in balance. A neutron is slightly heavier than a proton. The difference, written as an energy, is

$$Q = 1.293\ \text{MeV}$$

In the first second, while the temperature was above about 1 MeV, neutrons and protons were turned into each other all the time by the weak force, and the two kinds were kept in balance. Because the neutron is the heavier of the two, it is the rarer, by a factor that depends on the temperature $T$:

$$\frac{n}{p} = e^{-Q/T}$$

At very high temperature the ratio is close to 1. As $T$ falls towards $Q$, neutrons become scarce.

Freeze-out. The reactions that keep the balance slow down steeply as the universe cools, much faster than the expansion does. At about 1 MeV they can no longer keep up, and the ratio is left where it was, at about

$$\frac{n}{p} \simeq \frac{1}{6}$$

This is called freeze-out. From then on the only thing that changes the ratio is that free neutrons decay, with a mean life of 879.4 seconds.

The deuterium bottleneck. The first step in building helium is a proton and a neutron joining to make deuterium, which is held together by 2.23 MeV. You might expect that to begin as soon as the temperature fell below 2.23 MeV. It does not, because there are well over a billion particles of light for every proton or neutron. Even when the typical one is too feeble to break deuterium apart, enough of the rare energetic ones remain to do it. Deuterium only survives once the temperature is down to about 0.1 MeV, a little over a billion kelvin. By then enough neutrons have decayed that

$$\frac{n}{p} \simeq \frac{1}{7}$$

Counting the helium. Once deuterium survives, the rest goes quickly, and nearly every neutron ends up in helium-4. Each helium nucleus takes two neutrons and two protons, so the fraction of all the mass that ends up as helium is

$$Y_p = \frac{2\,(n/p)}{1 + n/p}$$

With $n/p = 1/7$ this is $\tfrac{2}{7} \div \tfrac{8}{7} = 0.25$. The measured value is $Y_p = 0.245 \pm 0.003$.

The answer hardly depends on how fast the nuclear reactions go. It depends on the mass difference $Q$, the neutron’s lifetime and the rate of expansion, which is why the helium fraction is such a clean test.

Why it stopped at helium. There is no stable nucleus with five particles and none with eight. Adding a proton or a neutron to helium-4, or joining two helium-4 nuclei, makes nothing that lasts. By the time this mattered, ordinary matter was no denser than air, and the building stopped. Stars do get past the gap, much later, by fusing helium into carbon in their dense cores.

The traces. The small amounts left over do depend on the reaction rates, and on how much ordinary matter there was. Deuterium is the most useful. The measured amount is

$$\mathrm{D/H} = (25.47 \pm 0.29) \times 10^{-6}$$

by number. Matching it fixes the number of protons and neutrons for every particle of light at about $6 \times 10^{-10}$. The oldest light gives the same number by a completely separate route. Lithium does not fit: the prediction for $^7\mathrm{Li/H}$ is 3.1 times the $(1.6 \pm 0.3) \times 10^{-10}$ found in old stars.

The colour of the oldest light. A blackbody at temperature $T$ is brightest at a wavelength

$$\lambda_{\text{peak}} = \frac{b}{T}, \qquad b = 2.898\ \text{mm K}$$

At 2.725 K this gives 1.06 mm, in the microwaves. At 3,000 K it gives 0.97 micrometres, just beyond the red end of what the eye can see. The two temperatures differ by a factor of about 1,100, and so do the wavelengths: the light has been stretched by exactly as much as it has cooled. These last figures are worked out here from the two temperatures.