KAHIBARO
Table of Contents
The first nuclei in the universe
Primordial nucleosynthesis is the formation of the lightest atomic nuclei in the early universe. It happened very soon after the Big Bang, long before stars and galaxies formed. This process is also called Big Bang nucleosynthesis, often shortened to BBN.
The word nucleosynthesis means "making nuclei." In this chapter, the important idea is that the hot early universe acted like a natural nuclear reactor. As the universe expanded and cooled, protons and neutrons combined to make a small set of light nuclei, mainly hydrogen and helium, with tiny amounts of a few others.
When it happened
Primordial nucleosynthesis took place during the first few minutes of cosmic history. Before this time, the universe was so hot that stable nuclei could not survive. Any nucleus that formed was quickly broken apart by very energetic photons.
As the temperature fell, conditions became suitable for some nuclei to remain intact. The main period of nucleosynthesis occurred roughly from about 1 second to about 20 minutes after the Big Bang. After that, the universe became too cool and too dilute for significant further fusion during this early phase.
The basic ingredients
The main particles involved were protons, neutrons, electrons, photons, and neutrinos. For nucleosynthesis itself, the crucial nuclear building blocks were protons and neutrons.
A proton is the nucleus of ordinary hydrogen. A neutron has nearly the same mass as a proton, but no electric charge. Since nuclei are made from protons and neutrons, the amount of each present in the early universe strongly affected what elements could form.
At first, protons and neutrons were continuously changing into one another through weak interactions. As the universe expanded and cooled, these reactions became too slow to keep up, and the neutron to proton ratio began to freeze out.
Why neutrons became less common
Neutrons are slightly more massive than protons, so at lower temperatures nature favors protons. Also, free neutrons are unstable and decay with time. A free neutron can decay into a proton, electron, and antineutrino.
Because of this, by the time nuclei began forming efficiently, there were fewer neutrons than protons. A useful rough value is that there was about 1 neutron for every 7 protons at the onset of effective nucleosynthesis.
This ratio is very important because almost all surviving neutrons ended up locked inside helium nuclei.
A key fact of primordial nucleosynthesis is that the final helium abundance is set mainly by the neutron to proton ratio just before nuclei form.
The deuterium bottleneck
The first step toward heavier nuclei is usually the formation of deuterium. Deuterium is a hydrogen nucleus with one proton and one neutron, written as $^2\mathrm{H}$ or D.
A typical reaction is
$$
p + n \rightarrow D + \gamma
$$
where $\gamma$ represents a gamma ray photon.
Even after the universe cooled enough that this reaction could occur, there was still a problem. The universe contained enormous numbers of photons compared with baryons such as protons and neutrons. Many photons still had enough energy to break deuterium apart:
$$
D + \gamma \rightarrow p + n
$$
So deuterium could not survive at first. This delay is called the deuterium bottleneck. Only when the temperature dropped enough did deuterium begin to survive long enough for further nuclear reactions to happen.
This bottleneck explains why nucleosynthesis started a little later than one might first expect.
Building helium
Once deuterium became stable enough, nuclear reactions proceeded quickly. Deuterium could combine with protons or neutrons and eventually form helium nuclei.
Important pathways included reactions such as
$$
D + p \rightarrow {}^3\mathrm{He} + \gamma
$$
$$
D + n \rightarrow {}^3\mathrm{H} + \gamma
$$
followed by reactions that produced helium 4:
$$
{}^3\mathrm{He} + n \rightarrow {}^4\mathrm{He} + \gamma
$$
$$
{}^3\mathrm{H} + p \rightarrow {}^4\mathrm{He} + \gamma
$$
Helium 4, written as $^4\mathrm{He}$, is especially stable. Because of this stability, once nucleosynthesis started in earnest, most available neutrons were rapidly incorporated into helium 4.
A helium 4 nucleus contains 2 protons and 2 neutrons. Since neutrons were the less abundant ingredient, they limited how much helium could be made.
Why mostly hydrogen and helium formed
The early universe produced mostly hydrogen and helium, not large amounts of heavier elements. There are two main reasons.
First, the universe was expanding rapidly. That meant there was only a short time window during which temperatures and densities were suitable for fusion.
Second, there are gaps in nuclear stability at mass numbers 5 and 8. In simple terms, it is hard to build stable nuclei with 5 nucleons or 8 nucleons under these early conditions. This blocked efficient production of heavier elements.
Because of these obstacles, primordial nucleosynthesis ended after making mainly light nuclei.
Big Bang nucleosynthesis produced mostly $^1\mathrm{H}$ and $^4\mathrm{He}$, with small amounts of deuterium, $^3\mathrm{He}$, and $^7\mathrm{Li}$. It did not produce the heavier elements in significant amounts.
Main products
The final abundances are usually described as fractions of the total ordinary matter. Most baryonic matter remained as hydrogen nuclei, and a substantial fraction became helium 4.
A simple summary is shown below.
| Nucleus | Common name | Approximate primordial abundance |
|---|---|---|
| $^1\mathrm{H}$ | Hydrogen | Most abundant |
| $^4\mathrm{He}$ | Helium 4 | About 25 percent by mass |
| $^2\mathrm{H}$ | Deuterium | Very small trace |
| $^3\mathrm{He}$ | Helium 3 | Very small trace |
| $^7\mathrm{Li}$ | Lithium 7 | Tiny trace |
The helium 4 mass fraction is often denoted by $Y_p$, and a typical predicted value is about
$$
Y_p \approx 0.25
$$
This means about one quarter of the mass of ordinary matter was produced as helium 4, while most of the rest remained hydrogen.
A rough way to understand this is to note that if the neutron to proton ratio is about $1:7$, then nearly all neutrons can pair up into helium 4. Since helium 4 contains 4 nucleons total, this leads naturally to a helium mass fraction near 25 percent.
A simple estimate of helium production
Suppose there are 7 protons and 1 neutron ratio, so in total there are 8 nucleons for every 1 neutron plus 7 protons. Since each helium 4 nucleus needs 2 neutrons, the number of helium nuclei is limited by the neutron supply.
If almost all neutrons end up in helium, then the fraction of nucleons in helium is approximately
$$
\frac{4 \times (\text{number of helium nuclei})}{\text{total number of nucleons}}
$$
With neutron fraction small but known, this gives a result close to
$$
Y_p \approx 0.25
$$
This is only a rough argument, but it shows why helium is abundant even though hydrogen remains dominant.
Temperature and time picture
It is helpful to connect the process to cooling.
| Time after Big Bang | Typical condition | What happens |
|---|---|---|
| Less than about 1 second | Extremely hot | Protons and neutrons interconvert rapidly |
| About 1 second | Cooler | Neutron to proton ratio begins to freeze out |
| A few minutes | Cool enough for deuterium survival | Nuclear reactions begin efficiently |
| Up to about 20 minutes | Density falling | Helium and light nuclei form |
| Later | Too cool and dilute | Primordial nucleosynthesis effectively ends |
Why deuterium is especially important
Deuterium is very useful for testing cosmology. Unlike helium, which is produced in large amounts and can also be altered in stars, deuterium is fragile. It is easily destroyed inside stars and not significantly created there in ordinary circumstances.
This means that when astronomers observe deuterium in very old, nearly unprocessed gas, they are seeing something close to its primordial abundance. That makes deuterium an excellent probe of early-universe conditions.
In particular, the primordial deuterium abundance is sensitive to the baryon density of the universe. If there were more baryons, nuclear reactions would proceed more efficiently and leave behind less deuterium.
Higher baryon density leads to more efficient fusion during BBN and usually leaves a lower leftover deuterium abundance.
The baryon density connection
One of the great successes of modern cosmology is that primordial nucleosynthesis links nuclear physics to the amount of ordinary matter in the universe.
The predicted abundances depend mainly on the baryon to photon ratio, often written as $\eta$. This quantity measures how many baryons exist compared with photons in the universe.
A larger $\eta$ means matter was denser relative to radiation during nucleosynthesis. That changes how efficiently the nuclear reaction network ran. By comparing predicted abundances with observed abundances, scientists can infer the cosmic baryon density.
This is powerful because it gives a completely different way to measure ordinary matter than methods based on galaxies or the later universe.
Observational evidence
Astronomers test primordial nucleosynthesis by measuring the abundances of light elements in places that have changed as little as possible since the early universe.
Hydrogen and helium are measured in old gas clouds and primitive galaxies. Deuterium is observed in distant gas clouds seen in absorption against bright background sources. Lithium is studied in old stars, though this case is more complicated.
The broad agreement between predicted and observed abundances, especially for helium and deuterium, is one of the strongest pieces of evidence for the Big Bang model.
The lithium problem
Most features of primordial nucleosynthesis agree well with observation, but lithium presents a puzzle. Standard calculations predict more lithium 7 than is observed in many old stars.
This mismatch is called the lithium problem. It may be related to how stars change their surface lithium over time, or it may hint at new physics beyond the simplest model. The issue is still studied.
Why primordial nucleosynthesis matters
Primordial nucleosynthesis is important for several reasons. It explains why the universe contains so much hydrogen and helium. It provides evidence that the universe was once extremely hot and dense. It allows measurement of the baryon density of the cosmos. It also tests particle physics in conditions that cannot be reproduced on large cosmic scales today.
Together with the cosmic microwave background and the expansion of the universe, primordial nucleosynthesis is one of the central pillars of Big Bang cosmology.
A visual timeline
Final picture
The story of primordial nucleosynthesis is simple in outline. The early universe cooled from an extremely hot state. Protons and neutrons were available as raw material. Deuterium could not survive at first, but once the temperature dropped enough, fusion began. Most neutrons were captured into helium 4, leaving a universe made mostly of hydrogen and helium, with tiny traces of a few other light nuclei.
Primordial nucleosynthesis is a major success of the Big Bang model because the predicted light-element abundances closely match what we observe in the universe today.