The simple model universes were selected for discussion because they provide a straightforward explanation for the origin of both the element helium and the cosmic background radiation, and because of their lack of complicating features. Nevertheless, it is by no means a simple task to discover all of their properties and construct cosmic histories which may possibly be confronted with observation. So, in order to set the scene, let us begin by tracing the history of such a model universe, and looking at its principal features. First of all, consider what it is like at the age of about 25 seconds. According to the simple model, its temperature is about four billion degrees, and its density roughly 2 tonnes per litre! At this time the principal constituents are radiation (photons) and neutrinos, with a very small admixture of matter in the form of protons, neutrons and electrons. The density of the matter component is less than 0.01 kg per litre, some ten times .the density of air at sea-level. Since radiation vastly outweighs the matter, the Universe is said to be radiation-dominated. The protons cannot combine with either the electrons (to form hydrogen atoms) or the neutrons (to form deuterium): such products would be broken apart by the intense radiation almost as soon as they were formed at this time. It is not until the Universe is some 200 seconds old that the radiation temperature has fallen enough to allow deuterium to form, and it is another million years before the electrons can combine with the protons to form neutral hydrogen gas (the EPOCH OF NEUTRALIZATION).

These two events, the synthesis of deuterium and the combination of electrons and protons, mark two very important events in the history of the Universe. With the onset of deuterium formation, nucleosynthesis begins abruptly and a chain of nuclear reactions takes place that converts almost all of the deuterium that is formed into helium. Within a matter of minutes, one quarter of the matter in the Universe is turned into helium. The other event, the formation of neutral hydrogen, marks the end of a radiation era and. as we shall see. the beginning of the era of galaxy formation. Once all the electrons have combined with the protons, the cosmic radiation field

Let us consider in a little more depth the significance of the nucleosynthesis period in terms of the simple cosmological models and of the Universe in which we live. The simple models indicate that between 25 and 27 per cent of the mass in the Universe was converted into helium. Not only is helium very difficult to destroy, it is also very difficult to make in stars in significant quantities. If our simple models of the universe were reasonable representations of the real Universe, astronomers should see an almost uniform abundance of the element helium, there being nowhere less than 25 per cent or so by mass. This is indeed what is seen. Not only is this regarded as strong evidence in favour of the simple models we have considered, but also as an indication that our extrapolation of the laws of physics so far into our past may not be unreasonable. Moreover, it is possible to compute the yield of helium expected from different cosmological models. Some of these contain mag¬netic fields, some have antimatter, and others rotate; but most do not produce the required quantity of helium.

It is now thought that most of the isotope deuterium must have been made in the early Universe. This is because astrophysicists have not yet been able to find a way of making the required quantity of deuterium in stars without at the same time making much more beryllium and boron than is observed. In cosmological nucleosynthesis, the deuterium that is left over is just a small amount that was not consumed in the making of helium and other elements. If we make the assumption that the observed deuterium is of cosmological origin, the logical question to ask is: do our simple models produce the required amount? Now we come to a very sensitive test of the simple model universes. The fraction of the Universe that is turned into helium is about 25 per cent in all simple models whose present mass density lies in the range one atom per 10000 litres to one atom per 100 litres. The helium observation does not allow us to distinguish observationally the open and closed models. However, whereas one atom in every 105 or so left over from the nucleosynthesis era in the open model is a deuterium atom, only one in every 1010 is a deuterium atom in the closed model. The observed deuterium abundance is nearer to one part in 105, and so the open simple model is strongly favoured if we believe the deuterium we observe is of cosmological origin.

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