I grant you that no sounds are given forth, but I affirm . . . that the movements of the planets are modulated according to harmonic proportions.
-- Johannes Kepler, 1619
Kepler's harmonic law of planetary motions owed more to geometry than to music, but the latest word on the cosmic microwave background (CMB) shows he would have been right about the universe as a whole.
The MAXIMA, BOOMERANG, and DASI collaborations, which measure minute variations in the CMB, recently reported new results at the American Physical Society meeting in Washington, D.C. All three agree remarkably about what the "harmonic proportions" of the cosmos imply: not only is the universe flat, but its structure is definitely due to inflation, not to topological defects in the early universe.
The results were presented as plots of slight temperature variations in the CMB that graph sound waves in the dense early universe. These high-resolution "power spectra" show not only a strong primary resonance but are consistent with two additional harmonics, or peaks.
MAXIMA and BOOMERANG were balloon-borne experiments that mapped parts of the sky over East Texas and Antarctica respectively. First findings were reported a year ago, but the new analyses include much more data in the case of BOOMERANG and greatly refined data in the case of MAXIMA. The DASI collaboration is a ground-based experiment at the South Pole whose results were reported for the first time at the Washington meeting.
Last year both BOOMERANG and MAXIMA clearly showed strong fluctuations on a scale of about one degree -- the first "peak" in the CMB power spectrum -- but only hinted at a second peak. In the new analyses, the power in the second peak region is clearly shown and the height of a third peak is suggested.
MAXIMA-1 WAS LAUNCHED FROM NASA'S NATIONAL SCIENTIFIC BALLOON FACILITY AT PALESTINE, TEXAS IN AUGUST, 1998
The peaks indicate harmonics in the sound waves that filled the early, dense universe. Until some 300,000 years after the Big Bang, the universe was so hot that matter and radiation were entangled in a kind of soup in which sound waves (pressure waves) could vibrate. The CMB is a relic of the moment when the universe had cooled enough so that photons could "decouple" from electrons, protons, and neutrons; then atoms formed and light went on its way.
At the moment of decoupling, the pressure waves left telltale traces of their existence in the form of slight temperature variations in the CMB, which in the intervening 10 billion years or so has cooled to a mere three degrees Kelvin. In 1992 George Smoot, a member of the Physics Division and a professor of physics at UC Berkeley, led the team that first detected fluctuations in the CMB with an experiment aboard the Cosmic Background Explorer satellite, COBE.
"Since the initial COBE mapping, many ground and balloon-based experiments have shown that the fluctuations have a peak in power at about one angular degree," says Smoot, who is a member of the MAXIMA collaboration.
Not exactly the music of the spheres
Analogous to the "first harmonic" of a vibrating string, the peak showed up strongly on the initial results from MAXIMA and BOOMERANG, indicating features of one angular degree -- indicating that the universe is flat. Had the variations been smaller or larger than a degree, they would have indicated a universe whose geometry is negatively or positively curved, like the surface of a saddle or a sphere.
The width and position of the first peak indicate that fluctuations on all scales were already in place at the earliest moments of the universe. A period of rapid expansion in the early moments of the universe could have set these perturbations in place by blowing up microscopic quantum fluctuations to astronomical scales -- seeding the galaxies and nets of galaxies we see today.
This explanation implies that there should be fluctuations at other scales as well, forming additional peaks on the power spectrum at half the fundamental scale, a third the fundamental scale, and so on. Last year neither BOOMERANG nor MAXIMA claimed to have observed a second peak, although their initial analyses were highly suggestive of one.
Digging deeper in the data
BOOMERANG, whose initial analysis was based on only half the information from one channel of its instrument, has now analyzed the data from four channels and plotted finer features with much greater certainty. Meanwhile, by rigorously eliminating noise, the MAXIMA collaborators produced a high-resolution map with pixels just one twentieth of a degree wide -- resolution nearly twice as fine as their initial map. Both new analyses clearly show the power in the second peak and suggest the height of the third -- as does DASI.
Had the structure of the universe been seeded not by inflation but by topological defects, that is by phase changes in the extreme energies of the early universe, the first peak in the CMB power spectrum would have been broader and lacking harmonics.
Instead, the new results show that the second peak is not pronounced, but the third is prominent and may even be elevated -- if so, one explanation could be that the universe contains slightly more baryons (ordinary matter) than currently predicted by models of the synthesis of light elements in the Big Bang.
Julian Borrill, an astrophysicist in NERSC, devised the MADCAP software package used in the initial analysis of both MAXIMA and BOOMERANG and the re-analysis of MAXIMA. "The new results really constrain the possible values of the fundamental parameters of cosmology," says Borrill, who is a member of both teams. "Last year, with only one clear peak, we had flatness and not much more. More peaks give us much more leverage to determine the parameters precisely."
MAXIMA is led by Paul Richards of Berkeley Lab's Materials Sciences Division and Adrian Lee of the Physics Division, both in the physics department at UC, and by Shaul Hanany of the University of Minnesota. BOOMERANG's U.S. collaborators are led by Andrew Lange of Caltech.
THE CMB POWER SPECTRUM ABOVE, PRODUCED BY MAXIMA, SHOWS A PRIMARY RESONANCE AND IS CONSISTENT WITH TWO MORE PEAKS; THEIR POSITION AND AMPLITUDE STRONGLY SUPPORT THE INFLATIONARY BIG BANG MODEL.
THE TEMPERATURE VARIATIONS IN EARLY UNIVERSE SEEN IN THE BOOMERANG IMAGES ABOVE ARE DUE TO SOUND WAVES IN THE PRIMORDIAL PLASMA. THE ANGULAR SPECTRUM OF THESE IMAGES SHOWN HERE, REVEALS THE CHARACTERISTIC SIZE OF THE STRUCTURES THAT DOMINATE THE IMAGE. A PEAK IN THIS SPECTRUM AT SCALES OF ~ 1 DEGREE, AS IS SEEN HERE IN THE BOOMERANG DATA, INDICATES THAT THE UNIVERSE IS NEARLY SPATIALLY FLAT. THIS GRAPH IS A "DOUBLE-BINNED" PLOT. THE RED POINTS ARE INDEPENDENT OF EACH OTHER, AS ARE THE BLUE POINTS. HOWEVER, EACH RED POINT IS BASED ON SOME OF THE SAME DATA AS ITS BLUE NEIGHBORS, AND VICE VERSA. THEREFORE NEIGHBORING POINTS ARE CORRELATED.