From radiation to matter

The hot Big Bang

The Big Bang theory says the universe began about 13.8 billion years ago in an extremely hot, dense state and has been expanding and cooling ever since. It was not an explosion of matter into empty space. Space itself has been stretching everywhere at once, and there is no centre.

The early universe was dominated by radiation: high-energy photons, along with particles moving so fast they behaved like radiation. As space expanded, every photon's wavelength was stretched, so its energy fell. Temperature is a measure of the typical energy of the particles and photons, so the universe cooled. A useful rule is that the average photon energy is about $2.7kT$, where $k = 8.62 \times 10^{-5}$ eV K⁻¹ is Boltzmann's constant.

The key idea of this page: as the universe cooled through particular temperatures, the photons no longer had enough energy to do certain things. Each of those thresholds left something behind, and together they explain where matter came from.

Mass–energy equivalence

Einstein's special relativity showed that mass and energy are two forms of the same thing. A mass $m$ is equivalent to an energy

$$E = mc^2$$

where $c = 3.00 \times 10^{8}$ m s⁻¹. Because $c^2$ is enormous ($9.00 \times 10^{16}$), a tiny mass corresponds to a huge energy. The equation runs both ways: matter can be converted to energy (as in stars and reactors), and energy can be converted into matter, as long as the conservation laws are obeyed.

In nuclear and particle physics, energies are usually given in electron volts. One electron volt is the energy an electron gains moving through 1 V: $1\ \text{eV} = 1.602 \times 10^{-19}$ J. Masses of atoms are given in unified atomic mass units, $1\ \text{u} = 1.661 \times 10^{-27}$ kg, and the data sheet gives the shortcut

$$1\ \text{u} = 931.5\ \text{MeV}/c^2$$

so multiplying a mass in u by 931.5 gives its energy equivalent in MeV.

Pair production and annihilation

A photon with enough energy can turn into a particle and its antiparticle. This is pair production. The most common example is a gamma-ray photon becoming an electron and a positron (an anti-electron, same mass, opposite charge):

$$\gamma \rightarrow e^- + e^+$$

Charge is conserved (0 = −1 + 1). The photon must have at least the rest energy of both particles, $2 \times 0.511 = 1.022$ MeV. In practice pair production happens near a nucleus, which recoils and lets momentum be conserved too.

The reverse is annihilation: a particle meets its antiparticle and they convert entirely into photons, usually two gamma rays of 0.511 MeV each heading in opposite directions. PET scanners in hospitals detect exactly these photon pairs from positrons emitted inside the body.

In the early universe, photons were energetic enough to make pairs constantly, and pairs annihilated just as often. Matter and radiation were in balance. Once the temperature fell so that typical photons had less energy than a pair's rest energy, pair production stopped, but annihilation carried on. Almost all the particles and antiparticles destroyed each other.

Almost all, but not quite. For roughly every billion antiquarks there were a billion and one quarks. That tiny excess, whose cause is still one of the big open questions in physics, is all the matter in the universe today. The billion annihilated pairs survive as the photons of the cosmic microwave background, which is why photons outnumber protons by about a billion to one.

From quarks to atoms

You met a simple Big Bang timeline in Year 10. At HSC level you need to explain why each stage happens when it does, using energy and temperature.

Big Bang nucleosynthesis

Within the first few minutes, neutrons and protons combined. The first step, $p + n \rightarrow {}^2\text{H} + \gamma$, could not stick until photons were too weak to break deuterium apart again (its binding energy is only 2.2 MeV). Once deuterium survived, almost every neutron ended up inside helium-4, which is very tightly bound.

A simple count shows how this predicts the composition of the universe. With about 1 neutron for every 7 protons, take 16 particles: 2 neutrons and 14 protons. The 2 neutrons join 2 protons to make one helium-4 nucleus (mass 4), leaving 12 protons as hydrogen (mass 12). Helium is $4/16 = 25\%$ of the mass. Astronomers measure about 24–25% helium by mass in the oldest gas clouds and stars, a strong confirmation of the Big Bang model.

Nothing heavier than lithium was made in useful amounts, because there are no stable nuclei with mass 5 or 8 to step through, and the universe cooled too quickly. Every heavier element was made later, in stars (page 8E).

Recombination and the cosmic microwave background

For 380 000 years the universe was a glowing plasma, opaque like the inside of the Sun, because photons scattered off free electrons. At about 3000 K, typical photons could no longer ionise hydrogen (13.6 eV), electrons and nuclei combined, and the universe became transparent. Those photons have been travelling ever since. Expansion has stretched their wavelengths by a factor of about 1100, so they now look like black-body radiation at 2.725 K, peaking in the microwave region.

The cosmic microwave background is evidence for the Big Bang because it is a near-perfect black-body spectrum, it comes equally from every direction (to 1 part in 100 000), and its temperature matches the predicted cooling. The tiny ripples in it, mapped by the COBE, WMAP and Planck satellites, are the seeds that grew into galaxies.

Measurements from the Planck satellite (2018) show that today the universe's energy is about 68% dark energy, 27% dark matter and only 5% ordinary matter made of atoms. Dark matter and dark energy are not explained by the Standard Model, and finding what they are is an active area of research.