Figure 10.6 HigFw super novae observed with the Hubble Space Telescope Courtesy of Peter ChaUiS, High-r team/NASA
Figure I f.3 Fluctuations in the microwave background from the BOOMERANG balloon experiment, "(lie measurements form a map of the variations in the microwave background The angular sire of the fluctuations tells the cosmic geometry, which agrees best with a fat universe in which I1 = £V^ 12,= 1 Courtesy of the BOOMERANG collaboration.
sion velocities for spiral nebulae were the effect of A at work, perhaps accelerating the galaxies from rest.
But there are more possibilities. If you have some dark matter, am, and some dark energy, QA, mathematical solutions to Finstein's equations have complicated and interesting properties. If £2m and Q.a have just the right values, the universe would expand, slow down under the influence of gravitating matter to almost zero speed, and the universe could loiter there before the repulsive effect of A would initiate an era of accelerating expansion. Before Hubble established the velocity-distance relation, this model had the feature, then thought to be desirable, of a long static period with no expansion, as Einstein had imposed in 1917.
The essential point is that a universe with both Q and A has a more complicated relation between the present rate of expansion, Hai and the cosmic age, L. In the decelerating phase, the universe would be younger than l/Ha. In the quasi-static phase, Ha would be near zero, and the universe would appear, like ill-mannered party guests who have overstayed their welcome, as if it would linger there forever, even though it had a finite age. In the accelerating phase, the then-current rate of expansion Hl} would be above the average, like a runner sprinting for the finish, and the elapsed time since the Big Bang could be longer than you'd compute from 1/H„. Like a game show host who has had a facelift, an accelerating universe would appear younger than it really is.
When Eddington was talking about loopholes to reconcile the (wildly mistaken) long ages of stars in rhe 1930s with the (wildly mistaken) short expansion age of the universe in 1931, he was thinking of the way that adjusting A could fix this problem. In polite circles, and even in astronomical discussions, using A to reconcile problems with timescales went the way of spats on shoes. They were kept in the attic as a relic of the 1920s, brought out on special occasions just for fun, but never worn at a serious event—until about 1996 when some fashion leaders tried them on at Princeton. We may all be wearing spats again.
A gravitating mass density equal to one has attractive mathematical properties, just as HA has been regarded as ugly. Following Ein stein's example, theorists look for the simplest formulations, with confidence that nature will follow (or, more precisely, precede) their good taste. If the mathematics looks beautiful, theorists take that as a sign they are on the right track. A "standard cold dark matter" universe with = 1 has a greater esthetic appeal than a low-density universe in which the density just keeps getting lower, so that drifts toward zero. And it has a better look than a high-density universe (Qni greater than one) in which the density eventually grows uncontrollably when the universe begins to contract. Ugh! But, like the porridge, chair, and bed that Goldilocks prefers, the fim = 1 universe is just right, and a universe with Qm = 1 stays a universe with £im = 1 even as the universe expands and slows. For Cin, of exactly one, the density decreases at just the right rate so that the ratio of the actual density to the critical density remains constant. In the inflation picture, there's an inescapable reason for ii to be one: the immense expansion drives ii inexorably to this value by ironing out any curvature.
This esthetic argument grips the theoretical mind like a bear hug and has been very close to the center of the cosmological discussion for the past 20 years. Particle physicists call their picture of the realm of quarks and the forces that bind them "the standard model." Looking for a little reflected glory, theoretical cosmologists have referred to the = 1 possibility as the "standard cold dark matter model." This was a good rhetorical device. But, as we shall see, it has two problems. One is the cosmic timcscale. If the universe has been decelerating in the way a universe dominated by gravitating matter requires, then the age of the universe comes into conflict with the ages of stars. The other is that measured masses of galaxies give ftm, the density of dark matter associated with galaxies, well below one. So if the total ii really is one, but the density of gravitating matter is not one, something else must contribute very significantly to the density of the universe. What could that be?
One possibility is something that gravitates, but does not cluster with the galaxies. If matter is distributed smoothly, it could elude our measurements in clusters. This would be "hot dark matter" where the individual particles have such high speeds they don't fall in to the deep troughs of galaxy clusters. The problem with hot dark matter is that, if it is important, it would smear out the growing structures of the universe too much to make the lumpy universe we see in redshift surveys. Elaborate numerical calculations of the way that structure grows in the universe show that hot dark matter would make a much smoother universe than the one we observe. The large-scale distribution of galaxies seen in big redshift surveys simply can't be matched if hot dark matter is the most important constituent. In an extravagant universe, where all the possibilities seem to be present, we can't rule out some dark matter of this type, but we have good evidence written in the sky that there is not enough to make ii = 1.
Another possibility is that it could be the cosmological constant. The mass equivalent of the dark energy contributes to the total il as fiA It could help make the universe flat, but would not show up in measurements of the matter density S2m. You could have a dollop of dark matter and a dollop of dark energy to make a total Q of one. But there are good reasons to be wary of this siren's call. Are you sure you want to use something Einstein grew to regret?
Only in the last few years, as observations have grown more telling, have we been able to move from a debate based on esthetics to a discussion based on evidence. Observations have dragged us reluctantly Loward accepting the view that the universe is dominated by the strange properties of empty space. After all, Einstein did say of the cosmological constant, "observations will enable us in the future ... to determine its value." The future is now.
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