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models with different densities. These densities are expressed as the current density that would correspond to that early density. The stability of 4He makes its abundance relatively insensitive to the density. However, the deuterium abundance drops off sharply with increasing density. This is because the deuterium is so reactive that a higher density provides it with more opportunities to react and be destroyed. There is a smaller density dependence in the 3He.

The heavier elements (especially 7Li) become more important at higher densities. This is because the high densities provide more reactions capable of building up the heavier elements. For densities greater than pcrit, C, N and O become somewhat abundant, but are still many orders of magnitude below their current observed abundances. This means that their current abundances of these heavier elements must be explained by production in stars.

The density dependence of the relative abundances of various nuclei provides us with a way of determining the density of the universe. We can measure the relative abundances of certain nuclei, such as D/H. We then use a diagram, like Fig. 21.17, to find the current density to which that ratio corresponds. In measuring the current abundances of any nucleus, it is important to account for any modification that has taken place since the big bang. Most important, the effect of nuclear processing of D in stars must be taken into account. The abundances that we see now are the result of big-bang and stellar nucleosynthesis. When we want to talk about the results of bigbang nucleosynthesis alone, we speak of primordial abundances.

It is important to note that this type of study only gives us the density of nuclear matter (protons and neutrons) in the universe. That is because it is only the nuclear matter that could have participated in nuclear reactions. For example, if the dark matter is in the form of neutrinos (which only interact via the weak interaction), then it may be that the nuclear matter is insufficient to close the universe, but the dark matter is still sufficient.

Most of the studies relating abundances to the density of the universe have involved deuterium. The net effect of stellar processing is to destroy deuterium. This means that the current D/H is less than the primordial value. On Earth, the D/H abundance ratio is about 10~4. This means that for every deuterium nucleus there are 10 000 hydrogen nuclei. From Fig. 21.17, we see that this corresponds to a current density of 3 X 10~31 g/cm3, which is much less than pcrit. Of course, the abundances in the Solar System may not be typical of the rest of the galaxy.

The next step is to study interstellar D, in whatever forms it is found. Direct observations of atomic D can be done in the Lyman a line (and other Lyman series lines) in the ultraviolet. These lines are observed in absorption against stars. Since interstellar extinction is so high in the ultraviolet, we cannot study clouds that are very far away. The results in our general area of the galaxy are similar to the Solar System value. Optical lines in the lines of sight to certain quasars give a value of about one D nucleus for every 40 000 H nuclei. This gives us an idea of values outside our galaxy.

Another possibility is the observation of the equivalent of the 21 cm line from atomic D. For deuterium, this line is shifted from 21 cm to 90 cm. Unfortunately, at this wavelength synchrotron radiation from the galaxy, whose intensity goes up approximately as A2, provides strong interference.

A final possibility is the radio observation of molecules containing deuterium, such as DCN. When we measure the abundances of these molecules, we find that the D abundance seems quite high. However, we now know that this is a result of chemical reactions (especially ion-molecule reactions) involving D and H proceeding at different rates for certain molecules. Thus, the abundances of the molecules don't reflect the true D/H abundance ratio. The observation of molecules with D substituted for H tells us more about interstellar chemistry than it does about cosmology.

The general conclusion of all of these D/H experiments is that the density of nuclear matter is probably about 5% of the critical density. If this result is correct, it doesn't mean that the universe is open. It just means that nuclear matter is not sufficient to close it. There is an additional note concerning 3He. It also has an abundance that depends on density, though not as strongly as the D abundance does. If an atom of 3He has one electron removed, a single electron remains. This ion behaves somewhat like a hydrogen atom. It has a transition analogous to the 21 cm line, at a wavelength of 9 cm. This line has been detected in galactic HII regions, but more detailed analyses are needed before these observations can yield cosmologically significant information.

In this section, we have discussed only what happened between one second and three minutes. Earlier than one second the universe was so hot that the internal structure of the neutrons and protons is important. Before we can understand what happened when the universe was less than one second old, we must look at some important features of elementary particle physics.

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