by George Rhee
The Particle Zoo
To understand more of the early universe we need to briefly discuss the elementary particles. These particles are classified according to which forces of nature they respond to. We have so far encountered two properties of particles; charge and mass. Another property is spin. Spin can be measured and has whole number values (for example 1, 2) or fractional values (such as and ). Particles such as electrons have a spin of one half and are called fermions. Particles with integer spins are called bosons. Bosons and fermions behave in different ways when they are pushed close together.
Since like charges repel, and the atomic nucleus contains only positively charged particles and neutral particles, what holds the nucleus together? A force of attraction called the strong force overcomes the electric repulsion on small scales. We have a picture of the atom with an outer shell of electrons and a compact nucleus. The atomic nuclei can also react with each other. They can stick together in a process known as nuclear fusion. For elements lighter than iron, the fusion process releases energy, although it takes very high temperatures to get it going. It is this energy release that powers the Sun and most stars. The reason fusion reactions take place only at very high temperatures is that nuclei are positively charged and therefore repel each other. They have to approach each other at high speeds to overcome the repulsion and get close enough for the short range strong interaction that causes fusion to be felt. One might think of rolling a bowling ball up the side of a hill with a crater at the top. If the ball has enough speed if can make it to the top and settle in the crater. If the speed is too slow the ball will roll back down the hill. Temperature is a measure of the speed of particles hence the need for high temperatures for fusion to take place.
Another force, the weak force, plays a role in fission. We have now encountered the four fundamental forces of nature, the strong force, the weak force, electromagnetism, and gravity. Electromagnetism describes the phenomena arising from electric and magnetic forces which were united in one framework by James Clerk Maxwell. He showed that electromagnetic fields could propagate through space in the form of radiation that we see as light.
The fermion family of particles can be further subdivided into hadrons and leptons. The hadrons are strongly interacting fermions, whereas the leptons are weakly interacting fermions. Examples of leptons are electrons and neutrinos; examples of hadrons are protons and neutrons (protons and neutrons have spins of one half). It turns out that hadrons have structure. We believe them to be made of even more fundamental particles called quarks. Hadrons which consist of three quarks, are called baryons. Hadrons which consist of a quark antiquark pair, are called mesons. Antiquarks are an example of antimatter. Each particles has its own antimatter counterpart, a particle with opposite charge but identical mass. The electron’s counterpart is called a positron. The existence of the positron was predicted by Paul Dirac (1902–1984) who devised a theory combining quantum physics and relativity.
The particle terminology we have introduced is shown schematically in Fig. 2.4. Baryons will be the subject of further discussion and are the most common form of hadron. To keep things simple, we may think of neutrons and protons when we use the word baryon. Other baryons exist, but they are very-short lived particles and do not play a role in our story.
Fig. 2.4The particle terminology. For each particle its strongest interaction is shown. In general it has all the interactions to the right of its entry, so that baryons, for example, have electromagnetic and weak interactions in addition to their strong interaction. Fermions are shown in green and bosons are shown in blue
Is there such a thing as an elementary particle? The atoms were shown to have structure, then the nucleus was shown to have structure, and most recently, the constituents of the nucleus have been shown to have structure. We can ask ourselves whether a fundamental level of matter exists. Do the quarks themselves have structure? We cannot answer this question at the present time. We also cannot explain the masses of the particles. Experiments underway at the Large Hadron Collider in Geneva, Switzerland aim to test theories of the origin of particle masses.
The First Three Minutes
Calculations of the fusion rates in the early universe predict that after nucleosynthesis is complete, the atomic matter in the universe should consist of 75 % hydrogen by mass, with 25 % helium, and only traces of other elements. This remarkable prediction is in agreement with the observed chemical composition of the atmospheres of the oldest known stars. Let us take a closer look at the process of helium formation.
Initially the universe was so hot that neither neutral atoms nor even atomic nuclei could exist. At that point the universe consisted of a mix of radiation and particles as shown in Fig. 2.5. When the universe was about 2 min old, the temperature had ‘cooled’ to one billion Kelvin, much hotter than the center of the Sun. The density of the universe at this time is about half that of the air you breathe.
Fig. 2.5Less than 1 s after the Big Bang, densities are high and interactions happen quickly. Protons (red) can convert to neutrons (blue) in reactions involving positrons (yellow) electrons (brown) and neutrinos (green). Light particles (photons) are shown as orange wiggly lines. The reactions take place via the weak interaction, one of the fundamental forces of nature
When the universe had cooled down to one billion degrees, it was cool enough for deuterium to hold together. This is because at temperatures higher than this a proton colliding with a deuterium nucleus has enough energy to break it apart. This illustrates the general point that at lower temperatures, matter exists in bound structures, while at higher temperatures, matter exists in the form of individual particles flying around (see Fig. 2.6).
Fig. 2.6As the universe cools interactions freeze out. Residual neutrons (blue) combine with protons (red) to form Deuterium, Helium, and Lithium in the first few minutes after the Big Bang
The presence of deuterium enables helium to form at a rapid pace. The deuterium nucleus consists of one proton and one neutron. It is an isotope, having the same chemical properties as hydrogen, but with a nucleus that contains an extra neutron. We can write the formation of deuterium as an equation:
That is to say, a neutron (n) plus a proton (p) combine to form deuterium (D) and release energy in the form of light (γ). The last symbol on the line, γ, represents a photon or light particle. The reaction can go either way resulting in the formation or destruction of deuterium.
Once deuterium has formed, two particles of deuterium can combine to form a helium nucleus. There is a small window of opportunity for helium to form in the early universe. It must be cool enough that deuterium nuclei can survive, but hot enough that the deuterium nuclei can collide and form helium. It is remarkable that in the 14 billion years of the history of the universe there were a few minutes during which conditions were just right for nuclear fusion to take place. Fusion reactions don’t take place at room temperature because of the force of repulsion between positively charged atomic nuclei. As we described in our hill with a crater metaphor, the repulsive force must be overcome for the particles to get close enough together to feel the strong nuclear force, which is a short range force. It is only at high temperatures that nuclei collide with sufficient speed to get close enough to interact via the strong force.
Deuterium and the Formation of Helium
The formation of deuterium is critical to the formation of helium because a helium nucleus can form by the collision of just two deuterium particles. To form a helium nucleus spontaneously from protons and neutrons would involve four particles colliding at the same time. Accidents involving two cars occur much more frequently than accidents involving four cars. So it is with particle collisions.
Almost all the deuterium formed in the Big Bang is used to make helium nuclei. To calculate how much helium formed in the big bang we need to know how much deuterium was present in the early universe. This, in turn is determined by the number of neutrons relative to protons at the time of nucleosynthesis
.
Neutrons are neutral particles that have a mass slightly larger than that of the proton. A free neutron can decay into a proton and an electron through the following reaction:
The symbol stands for an antineutrino. The typical time for this reaction to take place is about 15 min. This is the time it takes for a free neutron in space to turn into a proton. Note that a neutron inside a nucleus is stable, it will not turn into a proton. It may seem strange to see this number that we use in everyday life being relevant to the early universe. Initially there are roughly equal numbers of protons and neutrons in the universe. The neutrons can turn into protons but there is a resupply of neutrons from protons colliding with neutrinos. As the temperature drops there are fewer neutrons relative to protons. By the time the universe is a few seconds old, proton-neutron interchanging reactions have been brought to an end because the density is low enough that neutrinos cease to interact with anything. After 2 min the universe is cool enough for the remaining neutrons to combine with protons to form deuterium. At this time there are 2 neutrons for every 14 protons in the universe. These neutrons are absorbed into deuterium, so there are 2 deuterium nuclei for every 12 protons in the universe, Almost all these deuterium nuclei then combine to form helium nuclei. The end result is that there is 1 helium nucleus for every 12 protons in the universe which amounts to one quarter of the mass of nucleons in the universe.
A helium nucleus consists of two protons and two neutrons. Essentially, all the neutrons in the universe available at the time of nucleosynthesis end up inside helium nuclei. The amount of helium in the universe is thus determined by the neutron-to-proton ratio at the time when deuterium forms. For example if the neutron-to-proton ratio had been zero,– that is, no neutrons–no helium would form at all. If the neutron to proton ratio had been one, then the universe would consist entirely of helium. The helium abundance is a strong prediction of the Big Bang theory. There is not much room for maneuver. If the universe started in a hot, dense phase, then one quarter of the mass of baryons must consist of helium nuclei. The fact that helium was produced in the Big Bang would also explain why the helium abundance does not vary much from one location to another in the universe.
After nucleosynthesis, the universe consisted of a mix of photons, electrons, protons, and helium and deuterium nuclei (Fig. 2.7). It was still much too hot at this time for atoms to form.
Fig. 2.7In the first 400,000 years after the Big Bang, temperatures are so high that electrons (brown circles) cannot join protons (red circles) or helium and deuterium nuclei to form atoms. This is because the photons (orange wavy lines) are energetic enough to knock eletrons away from atoms. During this period photons cannot travel far before interacting
There is just a little deuterium left over from the Big Bang because the production of helium does not completely use up all of the deuterium nuclei. We can use the abundance of deuterium seen today to estimate the density of baryons in the universe. For a higher baryon density there should be very little deuterium left, but for a lower baryon density, more deuterium should survive. The abundance of deuterium in the universe today implies a present baryon density of the universe of 0.2 atoms per cubic meter, about double the density of matter seen in stars and gas. Studies of the cosmic background radiation lead us to the conclusion that the total density of matter in the universe is 1.3 atoms per cubic meter. Putting together the two we are forced to conclude that most of the matter in the universe does not consist of ordinary atoms. The question of the nature of this non-baryonic dark matter in the universe is one of the major issues of cosmology.
The Nature of the Big Bang
Most cosmologists explain their observations within the framework of the Big Bang theory. Some theoreticians like to think about what happened at the earliest times, minute fractions of a second after the Big Bang, and even discuss how the Big Bang might have occurred. The theory of inflation purports to account for the starting conditions of the Big Bang. In particular it explains why the universe is expanding, why it is homogeneous, and, why on large scales the universe has a flat geometry. Variants of the theory also suggest that different parts of the universe each have their own elementary particles and constants of nature. These areas form a sort of foam with a bubble structure. This idea, known as the multiverse, purports to explain why the constants of nature seem fined tuned so that we can exist in the universe. For example if the strong interaction was slightly stronger, then two protons would be able to bind together and form helium without two neutrons. This would have happened in the early universe with the result that no hydrogen would remain to provide fuel for stars, and water could not exist. These coincidences have led the distinguished physicist Freeman Dyson to state that:
As we look out into the universe and identify the many accidents of physics and astronomy that have worked together to our benefit, it almost seems as if the universe must have known that we were coming.
In the multiverse picture, the constants of nature take a wide range of values. Intelligent observers exist only in those rare bubbles in which by pure chance the constants happen to be just right for life to evolve. These ideas are very speculative and make few predictions that we can test. Recently though, it has been suggested that these processes might leave their mark on the cosmic background radiation in a way that we could detect. An interesting prediction of the multiverse idea was that galaxies would form in regions where the dark energy density is comparable to the dark matter density, this is indeed the case in our observable universe and could be viewed as a prediction of the model since it predates the discovery of dark energy.
It has also been argued that the universe could have spontaneously been created out of nothing. In quantum theory any process which is not forbidden by the laws of nature has a finite probability of taking place. In this view there is no cause needed for the creation of the universe.
The Timeline of the Universe
The Big Bang theory states that the expansion of the universe began at a finite time in the past, in a state of enormous density and pressure. As the universe grew older it cooled and various physical processes came into play which produced the complex world of stars and galaxies we see around us. The history of the universe can be outlined as follows:
The earliest period that has any significance in cosmology is known as the Planck time. This amazingly small time interval is 10 − 43 of a second. After this time, general relativity can be used to describe the interaction of matter and radiation with space. Before the Planck time, we have no theory to describe the universe. We require an idea that incorporates the concepts of quantum physics and general relativity into one unified theory. Stephen Hawking and his colleagues work on such problems, but no definitive answer has been arrived at yet. 0 to 10 − 43 s: This takes us from the moment of the big bang up to the Planck time. We have no physical theory to describe the behavior of matter under the conditions that prevailed this early in the history of the universe.
10 − 43 to 10 − 35 s: During this time a slight excess of matter over anti-matter was produced. After the matter and antimatter annihilated, a small amount of matter was left over. Today there is only one baryon per billion photons in the universe.
10 − 35 to 10 − 6 s: The fundamental forces separate into four recognizable forces that we see today. At the end of this era, quarks combine to form hadrons (e.g. neutrons and protons) and mesons.
10 − 6 to 10 − 4 s: This is known as the hadron era. During this time, the baryons and antibaryons annihilated, resulting in a slight excess of baryons being left over to form the stars and galaxies that we see around us.
10 − 4 to 10 s: This is the lepton era. Leptons are particles that feel the weak interaction, such as the electron. At 0.1 s the neutron to proton ratio starts to tilt in favor of protons. At 1 s, neutrinos stop interacting with matter and each other. At 10 s the neutron to proton ratio became fixed, which in turn determined the deuterium and
hence the helium abundance in the universe.
Three to twenty minutes: Nuclear fusion occurs, producing helium and a little deuterium and lithium. The explanation of the helium abundance is one of the triumphs of the Big Bang theory. The big bang also explains the abundance of very small amounts of deuterium and lithium.
10 to 1011 seconds (3,000 years): This is the radiation era. Radiation dominates the energy density of the universe during this period.
1013 s (400,000 years): The universe becomes cool enough for neutral atoms to survive and thus become transparent. Radiation can travel freely though the universe with very little chance of being scattered or absorbed (see Fig. 2.8).
Fig. 2.8Four hundred thousand years after the Big Bang, the universe has cooled sufficiently that atoms can form for the first time and light can travel freely through the universe. We detect this light today as the cosmic background radiation. The atoms present at this time are almost all hydrogen and helium
1013 s to present: During this time, regions of the universe that are slightly denser than their surroundings begin to collapse and eventually form stars, galaxies and clusters of galaxies. With the formation of the first stars nuclear fusion reactions occur again inside these stars for the first time since the first few minutes of the universe.
The Evolution of the Universe
As the universe ages it evolves. From being hot enough to act as a furnace for nuclear reactions, the universe has cooled to a few degrees above absolute zero. From the inferno of the first 3 min the universe cooled to a temperature that allowed the first clouds of primordial gas to collapse, at which point the first stars formed. The focus of the largest ground based 8–10 m mirror telescopes and space telescopes is to get a direct window into the first billion years of the universe and observe the growth and evolution of the cosmic structures mapped out by stars and galaxies. Astronomers are currently discovering objects that are recognizable as galaxies at a redshift of about eight. The light from these objects was emitted when the universe was less than 5 % of its present age (see Fig. 2.3).
