7. THE BIG BANG

Shortly after World War II, Russian physicist George Gamow, now working at George Washington University in Washington, DC, began to think about what the universe might be like during its earliest moments. He realized that the Friedmann solutions implied that the universe had infinite density when the expansion began, some 10 billion years ago, and that if so, the primordial matter in the early universe (less than a minute old!) would be as dense as the matter in the interiors of stars.

Gamow was one of the pioneers in understanding the theory of nuclear fusion, and so he was interested in the nuclear reactions that might occur under such circumstances. He assumed that the primordial matter in the universe, which he called "Ylem", was composed of pure neutrons. The network of reactions begins with the decay of a neutron into a proton, an electron, and a neutrino*:

n ® p + e + u , (1)

*Strictly speaking, the reaction produces an antineutrino, but I will ignore the distinction between neutrinos and antineutrinos, which is not critical to the arguments that follow.

Reaction (1) takes place with a half-life of 10.2 minutes (half of the neutrons will decay in that time). It is followed shortly afterwards by the combination of a proton and a neutron to form a deuterium nucleus (a form of heavy hydrogen composed of a neutron and proton bonded together) and a gamma ray photon:

p + n ® d + g. (2)

Both of these reactions release energy and will heat the gas to hundreds of millions of degrees. At such temperatures, the deuterium nuclei will undergo further nuclear reactions with neutrons and protons such as:

The net result of these reactions will be a universe of pure helium. This result is grossly in conflict with astronomical observations, which show that the matter in the universe is 75% hydrogen. Then Gamow had a brilliant insight: he realized that if the universe was already filled with gamma rays, the radiation could prevent the buildup of heavy elements by driving reaction (2) in the reverse direction:

d + g ® p + n. (7)

If the density of gamma rays in the early universe is sufficiently high, reaction (7) will destroy the deuterium nuclei before they hit a proton and undergo reaction (3). Gamow could calculate that a sufficiently high density of gamma rays meant that the universe must be filled with blackbody radiation that had temperature greater than 10⁹ K until 20 minutes A.B.E. (after the beginning of the expansion). After 20 minutes, 3/4 of the neutrons would have decayed into protons. If all the remaining neutrons formed helium according to reactions (2 - 4), the resulting mass fraction of helium in the universe would be about 25%, which is roughly the observed value. As the universe expands, the radiation cools off. (You can regard this cooling as a consequence of the redshift of the gamma ray photons due to the cosmic expansion.) Gamow calculated that if the radiation had a temperature of 10⁹ K when it was 20 minutes old, it would have a temperature of about 25 K now.

To see how the temperature of the radiation in the early universe is related to its age, see Calculating the temperature of the universe when it was very young, by team 4.

But, in 1950, a Japanese astrophysicist, Chushiro Hayashi, pointed out a big flaw in Gamow's theory. One of Gamow's basic assumptions, that the universe was originally filled with neutrons and gamma rays, could not be correct. If the radiation had a temperature of 10⁹ K when the universe was 20 minutes old, it would have to be much hotter when the universe was much younger, say 1 second A.B.E. But if the radiation is hotter than 10¹⁰ K, the gamma rays will be sufficiently energetic to produce electrons and positrons (anti-electrons) by the reaction:

e⁺ + n ® p + u (9)

and the electrons will react with the protons to produce neutrons and neutrinos:

e^- + p ® n + u. (10)

Because reactions (8 - 10) must occur, it's impossible for the early universe to be filled with only neutrons and gamma rays. There will certainly be plenty of electrons, positrons, and neutrinos as well, and these reactions (as well as the reverse reactions) will cause the neutrons to switch back and forth rapidly to protons. It is reactions (9) and (10) and their reverse reactions, not the decay of neutrons (reaction 1), that determine the helium abundance of the universe. At about 1 second A.B.E., the radiation temperature drops below 10 billion degrees and reactions (9) and (10) become too slow to change neutrons back and forth into protons. At this time, there are about three times as many protons as neutrons. As the universe continues to expand, the radiation cools below a billion degrees and these neutrons can combine with protons to form deuterium and helium according to reactions (2 - 6). By three minutes A.B.E., these reactions have run to completion and, from that time on, the universe consists of about 75% hydrogen and 25% helium by mass.

After Hayashi pointed out the flaw in Gamow's theory, several other astrophysicists independently revised the theory of the hot big bang to include these reactions. (It seems that they were mostly unaware of each other's work.) The most important consequence of the revised theory was that it predicted that the left-over radiation from the cosmic fireball would now have a temperature of about 3 K, roughly 10 times lower than Gamow's original prediction of 25 K.

For a brief review of this scenario, see The Hot Big Bang, and for more details, see Big Bang Nucleosynthesis, by Ned Wright.

What the Big Bang theory tells us about dark matter: Some scientists have suggested that the dark matter in the universe might accounted for by MACHOS -- brown dwarf stars or planets in intergalactic space (see Lesson 8). Such objects might escape detection with present telescopes. But the results above are evidence to the contrary. The measurements of cosmic deuterium tell us about the density of the normal matter of the universe when it was only a few minutes old, when the matter and radiation had temperatures greater than billions of degrees. At that time no planets or brown dwarf stars could have existed -- they would be vaporized. So it appears that the measurements of cosmic deuterium rules out the idea that the dark matter could be planets or brown dwarfs.

The main difference between the big bang and a supernova explosion: As in the big bang, fusion reactions occur in stars when they burn and finally explode as a supernova. But a supernova produces many heavy elements, such as oxygen, iron, and uranium, while the big bang produces only hydrogen and helium, plus traces of deuterium and lithium. Why are the results of these explosions so different? The reason is that the physical conditions are very different during the two explosions. Most nuclear fusion reactions occur when the temperature is in the range of about a billion degrees, and these temperatures occur in both exploding stars and in the early universe. In an exploding star, the density is roughly 10⁸ g/cm³. At such densities and temperatures, the nuclear reactions will create all the known elements. But when the universe has temperatures near a billion degrees, the density of neutrons and protons is only about 1% that of air. At such low densities, the triple-alpha reaction (see Lesson 5) that is required to convert helium into carbon and other heavy elements is too slow to be effective. In the early universe, the buildup of heavy elements stops at helium.

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Last modified April 14, 2002
Copyright by Richard McCray