galaxies are moving away from us, using the Doppler effect. This can be done very accurately. However, the distances to the galaxies are not very well known because we can measure them only indirectly. So all we know is that the universe is expanding by between 5 percent and 10 percent every billion years. Our uncertainty about the present average density of the universe is even greater. Still, if we add up the masses of all the stars that we can see in our galaxy and other galaxies, the total is less than one hundredth of the amount required to halt the expansion of the universe, even for the lowest estimate of the rate of expansion.
But that is not the whole story. Our galaxy and other galaxies must also contain a large amount of "dark matter" that we cannot see directly but which we know must be there because of the influence of its gravitational attraction on the orbits of stars in the galaxies. Perhaps the best evidence of this comes from the stars on the outskirts of spiral galaxies such as our Milky Way. These stars orbit their galaxies much too fast to be held in orbit merely by the gravitational attraction of the observed galactic stars. In addition, most galaxies are found in clusters, and we can similarly infer the presence of yet more dark matter in between the galaxies in these clusters by its effect on the motion of the galaxies. In fact, the amount of dark matter greatly exceeds the amount of ordinary matter in the universe. When we add up all this dark matter, we still get only about one-tenth of the amount of matter required to halt the expansion. But there could also be other forms of dark matter, distributed almost uniformly throughout the universe, that we have not yet detected and which might raise the average density of the universe even more. For instance, there exists a type of elementary particle called the neutrino, which interacts very weakly with matter and is extremely hard to detect (one recent neutrino experiment employed an underground detector filled with fifty thousand tons of water). The neutrino used to be thought massless, and therefore to have no gravitational attraction, but experiments over the last few years indicate that the neutrino actually does have a very tiny mass that had previously gone undetected. If neutrinos have mass, they could be a form of dark matter. Still, even allowing for neutrino dark matter, there appears to be far less matter in the universe than would be needed to halt its expansion, and so until recently most physicists would have agreed that the second type of Friedmann model applies.
Then came some new observations. In the last few years, several teams of researchers have studied tiny ripples in the background microwave radiation discovered by Penzias and Wilson. The size of those ripples can be used as an indicator of the large-scale geometry of the universe, and they appear to indicate that the universe is flat after all (as in the third Friedmann model)! Since there doesn’t seem to be enough matter and dark matter to account for this, physicists have postulated the existence of another as yet undetected substance to explain it—dark energy.
To further complicate things, other recent observations indicate that the rate of expansion of the universe is actually not slowing down but speeding up. None of the Friedmann models does this! And it is very strange, since the effect of the matter in space, whether high or low density, can only be to slow the expansion. Gravity is, after all, attractive. For the cosmic expansion to be accelerating is something like the blast from a bomb gaining power rather than dissipating after the explosion. What force could be responsible for pushing the cosmos apart ever faster? No one is sure yet, but it could be evidence that Einstein was right about the need for the cosmological constant (and its antigravity effects) after all.
With the rapid growth of new technologies and grand new satellite-borne telescopes, we are
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