The new subject was examined again, beginning in 2001, when NASA launched the Wilkinson Microwave Anisotropy Probe. (In this case, “anisotropy” refers to how the temperature of the cosmic background radiation differs with direction.) “WMAP allowed us to see fluctuations all across the sky,” says Bennett, the satellite’s principal investigator. “That by itself, at least qualitatively, was evidence for inflation.” But WMAP found something else.
Analysts plot the distribution of the temperature variations on a graph they call the power spectrum (see graph, opposite). Peaks in the spectrum correspond to the greatest differences in temperature; the highest peak occurs at distances of one degree (about half the size of the full moon). You might think of this one-degree distance as the length between the trough and peak of a wave.
“Everything you see [in the graph] is the development of the universe since inflation,” says Bennett. “But the fact that there are extra fluctuations at the one-degree scale all over the sky—you’d say: Well, what coordinated that? And the answer is: Inflation coordinated that.”
Cosmologists have devised another test for the theory of inflation, based on the size of the areas showing temperature deviations. That size is related to the quantum fluctuations in the primordial universe; it represents the distance that sound waves generated by the fluctuations traveled in 370,000 years—the time between the end of inflation and the moment when the universe had cooled enough for photons, or light waves, to begin the journey outward.
Imagine the distance that the sound waves traveled as the short side of a very long, skinny triangle. “The long side [of the triangle] is the distance that light travels in the next 13.8 billion years to us,” says Lawrence. “You can see an angle as one distance divided by another, and we measure that angle very well.” The angle is one of the six parameters in the model the Planck team constructed.
And now we come to somewhat familiar territory. In high school geometry, students learn that the sum of the angles of a triangle is 180 degrees. But if the triangle is superimposed on a sphere, the sum is greater than 180 degrees; if superimposed on a shape with negative curvature, like a saddle, the sum is less than 180 degrees. Inflation predicts that the shape of the universe will be most like a flat piece of paper, where the sum of the angles in a triangle equals 180 degrees. And that is what both WMAP and Planck measured—though not in the three dimensional analogy just described, but rather in the four dimensional mathematics of space-time. “Everything in cosmology is in four dimensions, but none of us can picture four dimensions,” says Charles Bennett.
“The math describes it in four and we understand it in four, but we don’t picture it in four any more than you do. I mean, we don’t experience relativity either, but we know how to calculate it. We know it works.”
According to the latest measurements and calculations, the universe is flat. “I like to say, ‘As accurately as we can measure it, it’s consistent with flat,’ ” hedges Bennett. “There’s uncertainty about what you expect in a theory,” he says, a plus-or-minus margin, like the uncertainty in opinion polls. “Inflation doesn’t predict that the universe is exactly flat. If inflation went on forever, it would be exactly flat, but inflation ended. One thing that we know for certain is that we are not still inflating,” he laughs.
“Without inflation, you don’t expect [the universe] to be anywhere near flat. If you start with the universe being just off of flat, it will get more and more off of flat. To come back 13.8 billion years later and find that it’s still close to flat would be odd. I use the analogy of standing a pencil straight up on its tip. To come back 13.8 billion years later and find the pencil still like that: not likely.”
Like Lawrence, Bennett believes that the temperature variations that are seen at the largest scales are consistent with predictions. Other cosmologists argue that such features as the lopsidedness in temperature counter the premise that inflation smoothed the universe on broad scales, enforcing the same laws of physics everywhere. Those features also defy a basic cosmological principle: that space should look similar in all directions, and no place should be more “special” than another.