Where did the matter come from that makes up the galaxies, stars, planets and humans? Creation of the universe (the "big bang") includes the creation of space and the matter within it, so this question leads us to consider what kind of matter was initially created. Astronomical observations and cosmological theory together demonstrate that the varieties of matter created in the early universe determine the amount of helium (He) observed in the universe today.

Today's visible matter is made up of atoms. But atoms could not exist in the intense heat of the early universe. If time could be made to run backwards, the universe would become so hot that an atom would break up into a nucleus and electrons. By continuing to run the clock backwards, causing the temperature of the universe to increase, a nucleus would break up into its constituent protons and neutrons. A neutron would start to undergo radioactive decay into an electron and a less commonly known particle called a neutrino (more precisely, an anti-neutrino). Increasing the temperature of the universe even more (traveling further back in time) causes the break-up of neutrons and protons into quarks and the particles that ordinarily keep the quarks bound (gluons).

Let us consider the universe at this early stage of its evolution, when it is less than a millionth of a second old and is made up of photons (electromagnetic radiation causing the high temperature), neutrinos, quarks, electrons, anti-particles, and other particles that do not concern us now. Running the clock forwards to one millionth of a second, we find the universe cool enough so that the quarks coalesce into protons and neutrons.

When the universe is older than one millionth of a second, an extremely hot mixture (temperature of ten trillion Kelvin) of photons, neutrons (n), protons (p), electrons (e), neutrinos, anti-electrons, and anti-neutrinos participate in the reactions below.


More protons are created in these reactions because they are slightly less heavy than neutrons. These reactions occur until the expansion and cooling of the universe prevent the last two. One second after the big bang, when the universe had cooled to a temperature of less than 10 billion Kelvin, there were 6 times as many protons as there were neutrons.

Two protons and two neutrons are needed to make a helium nucleus, but the universe is still too hot to form He. A four-particle collision is not how a He nucleus is formed, however. He nuclei are formed from deuteron (a bound proton and neutron) collisions, but the universe must cool down to a temperature of 1 billion Kelvin for deuterons to form via the collision of a proton and neutron to give a deuteron and a photon.

Helium can now form in either one of the following two-step sequences.



While the universe was cooling to form deuterium, the neutrons were decaying so that only 80% of the initial number were left by the time of the deuteron collisions.


The mass fraction of helium in the universe can now be calculated. Recall that a helium nucleus consists of 2 protons and 2 neutrons. Therefore to get the number of total He nuclei, divide the total number of neutrons by 2 (2 neutrons make 1 He nucleus, 4 neutrons make 2 He nuclei, etc.). And because the masses of the proton and neutron are nearly the same, the mass of the He nucleus is approximately 4 times the mass of one neutron. Dividing this value by the mass of all neutrons and protons gives the mass fraction of He in the universe.

This calculated value corresponds closely to the observed value as shown in the graphs below (Izotov and Thuan, ApJ Letters, 710: L67-L71, 2010), another confirmation of the big-bang theory of the universe.

South Carolina State University, 01/24/2015
This material is based upon work supported by the National Science Foundation under Grant Number AST-0750814. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.