If the early Universe was very hot and very dense and all hydrogen, some of it ought to have fused and become helium, carbon, and other elements. The question, How much of each? was one that Gamow and his student, Ralph Alpher, set out to answer. They calculated that about a quarter of the matter in the primeval Universe should have turned to helium, a figure very consistent with the present composition of the oldest stars. They published their results on April 1, 1948. In one of physics’ best-known jokes, Hans Bethe (pronounced Bay-ter, like the Greek letter Beta) allowed his name to be added to the paper, although he had nothing to do with its writing. The authors thus became Alpher, Bethe, and Gamow.
Apart from showing how to calculate the ratio of hydrogen to helium after the Big Bang, Gamow and his colleagues did one other thing whose full significance probably escaped them. In 1948 they produced an equation that allowed one to compute the present background temperature of the Universe from its age, assuming a Universe that expanded uniformly since its beginning in the Big Bang. The background radiation, corresponding to a temperature of 2.7 degrees above absolute zero, was discovered by Arno Penzias and Robert Wilson in 1964, and made the Big Bang theory fully respectable for the first time.
We now believe that hydrogen fused to form helium when the Universe was between three and four minutes old. What about even earlier times? Let us run the clock backwards, as far as we can towards the Big Bang.
How far back do we want to start the clock? Well, when the Universe was smaller in size, it was also hotter. In a hot enough environment, atoms as we know them cannot hold together. High-energy radiation rips them apart as fast as they form. A good time to begin our backward running of the clock might then be the period when atoms could form and persist as stable units. Although stars and galaxies would not yet exist, at least the Universe would be made up of familiar components, hydrogen and helium atoms that we would recognize.
Atoms can form, and hold together, somewhere between half a million and a million years after the Big Bang. Before that time, matter and radiation interacted continuously, and the Universe was almost opaque to radiation. After it, matter and radiation “decoupled,” became near-independent, and went their separate ways. The temperature of the Universe when this happened was about 3,000 degrees. Ever since then, the expansion of the Universe has lengthened the wavelength of the background radiation, and thus lowered its temperature. The cosmic background radiation discovered by Penzias and Wilson is nothing more than the radiation at the time when it decoupled from matter, now grown old.
Continuing backwards, even before atoms could form, helium and hydrogen nuclei and free electrons could combine to form atoms; but they could not remain in combination, because radiation broke them apart. The content of the Universe was, in effect, controlled by radiation energetic enough to prevent the formation of atoms. This situation held from about three minutes to one million years A.C. (After Creation).
If we go back to a period less than three minutes A.C., radiation was even more dominant. It prevented the build-up even of helium nuclei. As noted earlier, the fusion of hydrogen to helium requires hot temperatures, such as we find in the center of stars. But fusion cannot take place if it is too hot, as it was before three minutes after the Big Bang. Before helium could form, the Universe had to “cool” to about a billion degrees. All that existed before then were electrons (and their positively charged forms, positrons), neutrons, protons, neutrinos (a chargeless particle, until recently assumed to be massless but now thought to possess a tiny mass), and radiation.
Until three minutes A.C., it might seem as though radiation controlled events. But this is not the case. As we proceed farther backwards and the temperature of the primordial fireball continues to increase, we reach a point where the temperature is so high (above ten billion degrees) that large numbers of electron-positron pairs can be created from pure radiation. That happened from one second up to fourteen seconds A.C. After that, the number of electron-positron pairs decreased rapidly. Less were being generated than were annihilating themselves and returning to pure radiation. After the Universe cooled to ten billion degrees, neutrinos also decoupled from other forms of matter.
Still we have a long way to go, physically speaking, to the moment of creation. As we continue backwards, temperatures rise and rise. At a tenth of a second A.C., the temperature of the Universe is thirty billion degrees. The Universe is a soup of electrons, protons, neutrons, neutrinos, and radiation. As the kinetic energy of particle motion becomes greater and greater, effects caused by differences of particle mass are less important. At thirty billion degrees, an electron easily carries enough energy to convert a proton into the slightly heavier neutron. Thus in this period, free neutrons are constantly trying to decay to form protons and electrons; but energetic proton-electron collisions go on remaking neutrons.
We keep the clock running. Now the important time intervals become shorter and shorter. At one ten -thousandth of a second A.C., the temperature is one thousand billion degrees. The Universe is so small that the density of matter, everywhere, is as great as that in the nucleus of an atom today (about 100 million tons per cubic centimeter; a fair-sized asteroid, at this density, would squeeze down to fit in a match box). Modern theory says that the nucleus is best regarded not as protons and neutrons, but as quarks, elementary particles from which the neutrons and protons themselves are made. Thus at this early time, 0.0001 seconds A.C. the Universe was a sea of quarks, electrons, neutrinos, and energetic radiation. We move on, to the time, 10-36 seconds A.C., when the Universe went through a super-rapid “inflationary” phase, growing from the size of a proton to the size of a basketball in about 5 x 10-32 seconds. We are almost back as far as we can go. Finally we reach a time 10-43 seconds A.C, (called the Plank time), when according to a class of theories known as supersymmetry theories, the force of gravity decoupled from everything else, and remains decoupled to this day.
This may already sound like pure science fiction. It is not. It is today’s science — though it certainly may be wrong. But at last we have reached the time when McAndrew’s “hidden matter” was created. And today’s Universe seems to require that something very like it exist.
The argument for hidden matter goes as follows: The Universe is expanding. Every cosmologist today agrees on that. Will it go on expanding forever, or will it one day slow to a halt, reverse direction, and fall back in on itself to end in a Big Crunch? Or is the Universe poised on the infinitely narrow dividing line between expansion and ultimate contraction, so that it will increase more and more slowly, and finally (but after infinite time) stop its growth?
The thing that decides which of these three possibilities will occur is the total amount of mass in the Universe, or rather, since we do not care what form mass takes and mass and energy are totally equivalent, the future of the Universe is decided by the total mass-energy content per unit volume.
If the mass-energy is too big, the Universe will end in the Big Crunch. If it is too small, the Universe will fly apart forever. And only in the Goldilocks situation, where the mass-energy is “just right,” will the Universe ultimately reach a “flat” condition. The amount of matter needed to stop the expansion is not large, by terrestrial standards. It calls for only three hydrogen atoms per cubic meter.