Those are good questions, and there is a good answer. First, recall that there are actually two types of dark matter: baryonic and non-baryonic dark matter. Baryonic matter (whether luminous or dark) is matter that is made up of neutrons and protons, including all the forms of matter that have ever actually been observed by physicists (with the exception of very lightweight elementary particles like electrons and neutrinos).
It is possible to compute approximately the total density of matter in the universe in several ways, but mainly by observing the motions of stars within galaxies and of galaxies within galaxy clusters. These observations tell us that there is far more matter out there than occurs in luminous objects such as stars and galaxies. It is quite possible, of course, that much or even most of the matter that isn't luminous is still "ordinary" baryonic matter.
But there is one good way to tell that this cannot be the case. It turns out that during a brief period in the very early universe, between about 5 minutes and 30 minutes after the big bang, almost all of the lightweight nuclei other than protons (ordinary hydrogen) were formed in a process called nucleosynthesis. The most abundant of these nuclei was ordinary helium: helium-4, consisting of 2 protons and 2 neutrons. This amounted to about 24% of baryonic matter, with almost all the rest being ordinary hydrogen (single protons). In addition, there were very small trace amounts of deuterium (hydrogen-2), tritium (hydrogen-3), helium-3, and lithium-7. Complex calculations make it possible to predict roughly what the proportions of each of these nuclei should be. Numerous observational studies have repeatedly confirmed these predictions, and this forms some of the most solid evidence for the whole big bang model of the origin of the universe.
In these calculations it happens that the very small proportion of deuterium depends very sensitively on the ratio of the number of baryons to photons that existed at the time nucleosynthesis began. Therefore, if we knew how much deuterium was formed, we could infer what this baryon-photon ratio was. Of course, we have no way to measure the amount of deuterium right after nucleosynthesis was complete. But because deuterium has a rather fragile nucleus, it is destroyed rather than created in stars. So a measurement of the amount of deuterium in the universe today gives a lower bound for what existed in the very distant past, and probably not a bad estimate, as long as one measures the abundance of deuterium in interstellar gas, most of which has not been inside a star.
Unfortunately, until recently, the only way to measure this abundance has been spectroscopically, at ultraviolet and optical frequencies. This is a problem because in those wavelengths the spectra of hydrogen and deuterium are very similar. They are much less similar at radio frequencies, and good RF measurements have just been announced by a research group at MIT: Researchers find clue to start of universe. The work was done at MIT's Haystack Observatory.
So, what's the bottom line? What was found is that the ratio of deuterium to hydrogen in the local interstellar medium implies a photon-baryon ratio of about 2 billion to 1. That is, there must be about 2 billion photons for every baryon. (See the graph at the bottom of this page for a graph of the relationship of photon-baryon ratio to deuterium-hydrogen ratio.) But it's relatively easy to determine the density of photons in the universe (from measurements of the cosmic microwave background). And so we can get the density of baryons in the universe. The result is that baryons can make up only about 15% of the mass of all gravitating matter in the universe. And hence the other 85% has to be non-baryonic dark matter.
These conclusions about the relative abundance of deuterium and hence the amount of non-baryonic dark matter are not new, but the measurements of deuterium in the interstellar medium provide an independent confirmation of earlier results.
Another article about this: Deuterium at the dawn of time
Original journal article: Deuterium Abundance in the Interstellar Gas of the Galactic Anticenter from the 327 MHz Line (subscription required for full access)
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