The Hot Big Bang

The big bang starts off with a state of extremely high density and pressure for the Universe. Under those conditions, the Universe is dominated by radiation. This means that the majority of the energy is in the form of photons and other massless or nearly massless particles (like neutrinos) that move at near the speed of light. As the big bang evolves in time, the temperature drops rapidly as the Universe expands and the average velocity of particles decreases.
Finally, one reaches a state where the energy of the Universe is primarily contained in non-relativistic matter (matter sufficiently massive that its average velocity is very much less than the speed of light). This is called a matter dominated universe. The early Universe was radiation dominated, but the present Universe is matter dominated. Let us now give a brief description of the most important events in the big bang.

The Cast of Characters for the Big Bang

The primary cast of characters includes:

1. Photons ("particles" of light)
2. Protons and neutrons
3. Electrons and their antiparticles the positrons
4. Neutrinos and their antiparticles the antineutrinos

Because of the equivalence of mass and energy in the Special Theory of Relativity, in a radiation dominated era the particles and their antiparticles are continuously undergoing reactions in which they annihilate each other, and photons can collide and create particle and antiparticle pairs. One says that under these conditions the radiation and the matter are in thermal equilibrium because they can freely convert back and forth. Let us now follow the approximate sequence of events that took place in the big bang in terms of the time since the expansion begins.

Time ~ 1/100 Second

At this stage the temperature is about 100 billion Kelvin and the density is more than a billion times that of water. The Universe is expanding rapidly and is very hot; it consists of an undifferentiated soup of matter and radiation in thermal equilibrium. This temperature corresponds to an average energy of the particles of about 8.6 MeV (million electron-Volts). The electrons and positrons are in equilibrium with the photons, the neutrinos and antineutrinos are in equilibrium with the photons, antineutrinos are combining with protons to form positrons and neutrons, and neutrinos are combining with neutrons to form electrons and protons. At this stage the number of protons is about equal to the number of neutrons.

Time ~ 1/10 Second

Now the temperature has dropped to several times 10 billion Kelvin and the density is a little over 10 million times that of water as the Universe continues to expand. Because a free neutron is slightly less stable than a free proton, neutrons beta decay to protons plus electrons plus neutrinos with a half-life of approximately 17 minutes. Thus, the initial approximately equal balance between neutrons and protons begins to be tipped in favor of protons. By this time about 62% of the nucleons are protons and 38% are neutrons. The free neutron is unstable, but neutrons in composite nuclei can be stable, so the decay of neutrons will continue until the simplest nucleus (deuterium, the mass-2 isotope of hydrogen) can form. But no composite nuclei can form yet because the temperature implies an average energy for particles in the gas of about 2.6 MeV, and deuterium has a binding energy of only 2.2 MeV and so cannot hold together at these temperatures. This barrier to production of composite nuclei, which allows the free neutrons to be steadily converted to protons, is called the deuterium bottleneck.

Time ~ 1 Second

The temperature has dropped to about 10 billion K as the Universe continues to expand, and the density is now down to about 400,000 times that of water. At this temperature the neutrinos cease to play a role in the continuing evolution, but the deuterium bottleneck still exists so there are no composite nuclei and the neutrons continue to beta decay to protons. At this stage the protons abundance is up to 76% and the neutron abundance has fallen to 24%.

Time ~ 13.8 Seconds

The temperature has now fallen to about 3 billion K. The average energy of the particles in the gas has fallen to about 0.25 MeV. This is too low for photons to produce electron-positron pairs so they fall out of thermal equilibrium and the free electrons begin to annihilate all the positrons to form photons. The deuterium bottleneck still keeps appreciable deuterium from forming and the neutrons continue to decay to protons. At this stage the abundance of neutrons has fallen to about 13% and the abundance of protons has risen to about 87%.

Time ~ 3 Min 45 Sec

Finally the temperature drops sufficiently low (about 1 billion K) that deuterium nuclei can hold together. The deuterium bottleneck is thus broken and a rapid sequence of nuclear reactions combines neutrons and protons to form deuterium, and the resulting deuterium with neutrons and protons to form the mass-4 isotope of helium (alpha particles). Thus, all remaining free neutrons are rapidly "cooked" into helium. Elements beyond helium-4 cannot be formed because of the peculiarity that there are no stable mass-5 or mass-8 isotopes in our Universe and the next steps in the most likely reactions to form heavier elements would form mass-5 or mass-8 isotopes.

Time ~ 35 Minutes

The temperature is now about 300 million K and the Universe consists of protons, the excess electrons that did not annihilate with the positrons, helium-4 (26% abundance by mass), photons, neutrinos, and antineutrinos. There are no atoms yet because the temperature is still too high for the protons and electrons to bind together.

Time ~ 700,000 years

The temperature has fallen to several thousand K, which is sufficiently low that electrons and protons can hold together to begin forming hydrogen atoms. Until this point, matter and radiation have been in thermal equilibrium, but now they decouple. As the free electrons are bound up in atoms the primary cross section leading to the scattering of photons (interaction with the free electrons) is removed and the Universe (which has been very opaque until this point) becomes transparent: light can now travel large distances before being absorbed.

Production of the Light Elements in the Big Bang

One important success of the big bang model has been in describing the abundance of light elements such as hydrogen, helium, and lithium in the Universe. These elements are produced in the big bang, and to some degree in stars. Analysis of the oldest stars, which contain material that is the least altered from that produced originally in the big bang, indicate abundances that are in very good agreement with the predictions of the hot big bang. One particularly sensitive test involves the abundance of deuterium. Because deuterium has a nucleus that is very weakly bound compared with most nuclei, it is very sensitive to the conditions in which it is formed (as we have just seen): if the temperatures are too high, deuterium breaks apart, and it can only be formed when there are free neutrons to combine with protons. Detailed analysis of the deuterium abundance gives very strong support to the hot big bang picture.

The Steady State Model

The big bang model had an early challenger that was called the steady state model. The steady state model did the cosmological principle one better by invoking what has been termed the perfect cosmological principle: Not only is the Universe the same at all places and in all directions when averaged over a large enough volume; it is the same for all time too. Since the Universe was known to be expanding, the steady state model had to postulate continuous creation of matter in the space between the stars and galaxies to maintain the same density over time and thus satisfy the perfect cosmological principle of a universe unchanging in time on large scales. This violates the law of mass-energy conservation, but the rate of mass creation that is required is far too small to be detectable by any conceivable experiment, so it cannot be ruled out experimentally (the rate that is required is to create approximately 1 hydrogen atom per cubic centimeter every 10¹⁵ years).

The Triumph of the Big Bang

For a time, the steady state theory and the big bang theory competed with each other, but eventually observations all but ruled out the steady state theory while providing strong support for the big bang. Probably the two most important observations were

1. Deep space radio telescope observations (which therefore peered far back in time because of the finite speed of light) indicating that the early Universe looked very different from the present Universe. For example, there appear to be more quasars at great distances, implying that there were more quasars in the early Universe than the present one. This contradicted the steady state hypothesis that the Universe was unchanging over time on large scales.
2. The discovery of the cosmic microwave background to be discussed shortly, that appeared to permeate all of space. This was an expected consquence of the big bang model, but was very difficult to explain in any simple way in the steady state theory.

As a consequence of these and other findings, the steady state theory is no longer considered viable by most astronomers.