Recombination (cosmology)

In the study of cosmology, recombination refers to a critical epoch in the early universe. This was the period when charged electrons and protons first became bound to form electrically neutral hydrogen atoms.

This transition changed the entire nature of the cosmos. Before this event, the universe was a hot, dense plasma. This plasma consisted of photons, leptons, and quarks. As the universe expanded, it also cooled. Eventually, the temperature dropped enough that neutral hydrogen atoms became energetically favored over free particles. This shift allowed the universe to move from an opaque state to one that was transparent.

To understand the mechanism, we must look at the state of the universe immediately after the Big Bang. During the quark epoch, the universe was a dense soup of fundamental particles. By 10⁻⁶ seconds, the universe had cooled enough to enter the hadron epoch, where protons could form. At this stage, the universe was effectively opaque to electromagnetic radiation. This was due to Thomson scattering, where photons constantly bumped into free electrons. This scattering meant the mean free path of a photon was very short. This environment is similar to the current state of the interior of our Sun.

As the expansion continued, the cooling led to the specific process of recombination. In this process, electrons bind to protons, which are the nuclei of hydrogen. However, these atoms do not always form in their lowest energy state, known as the ground state. Because of low wavefunction overlap, electrons generally form in a high energy state first. These electrons must then cascade through intermediate states to reach the ground state. They do this by emitting photons. There are two main pathways for this. One pathway involves the 2p state emitting a Lyman-alpha photon. These photons are usually reabsorbed by other hydrogen atoms. The second pathway involves the 2s state emitting two photons, though this has a much lower probability.

This emission of photons leads to a related event called decoupling, or photon decoupling. While recombination and decoupling are distinct, they are closely linked. Once photons decoupled from matter, they could travel freely through the universe without interacting with particles. This released light is what we observe today as the cosmic microwave background radiation (CMB).

When this light was first emitted, the universe was at a temperature of approximately 3,000 K. Because the universe has expanded since then, this radiation has undergone a redshift. It has shifted from the visible spectrum into the microwave spectrum.

Scientists can estimate the timing of recombination using the temperature of the CMB. The CMB follows a blackbody spectrum, which is a spectrum characterized entirely by its temperature. The shift in energy caused by the expansion of the universe is called redshift, denoted by the letter z. The temperature of the CMB today is 2.7 K. We can calculate the temperature at any redshift using the formula: T_CMB = 2.7 K × (1 + z). By evaluating the thermal equilibrium between matter and radiation, researchers can find the exact moment of recombination. This occurs when the density of photons with enough energy to ionize hydrogen matches the density of baryons.

Through these calculations, we know recombination occurred about 378,000 years after the Big Bang. This happened at a redshift of approximately z = 1100. The ratio of baryons to photons, known as eta (η), is measured to be around 10⁻⁹. This value was confirmed by measurements from the Planck satellite. To describe the history of this process, scientists use the free electron fraction, xe. This is the ratio of free electrons to the total abundance of hydrogen. As recombination progressed, the fraction of free electrons decreased to just a few parts in 10,000. This shows how effectively the protons and electrons joined together.

Historically, the term "recombination" is somewhat misleading. In modern Big Bang theory, protons and electrons were not combined before this era. The name exists because it was established before the Big Bang hypothesis became the primary theory of the universe's origin. Despite this, the term remains the standard way to describe this era. Recombination is a fundamental concept that connects particle physics to the large-scale structure of the universe. It explains how the universe transitioned from a glowing, opaque plasma into the transparent cosmos we can observe today through telescopes.