Cosmic Microwave Observations Yield More Evidence of Primordial Inflation

Last year, two balloon-borne bolometric telescopes--Boomerang and Maxima--spectacularly confirmed the large-scale Euclidean flatness of the universe by measuring the first "acoustic peak" of the fluctuation power spectrum of the cosmic microwave background (CMB). (See PHYSICS TODAY, July 2000, page 17.)

A compact microwave interferometer called DASI (DegreeAngular Scale Interfereometer), installed at the South Pole last year, has recorded a clear second acoustic peak and enticing evidence of a third. That's what cosmologists had been waiting for with eagerness and some trepidation. Flat cosmic geometry is just one of the central predictions of the widely accepted inflationary version of Big Bang cosmology. The inflationary scenario also requires a harmonic sequence of lesser acoustic peaks corresponding to CMB fluctuations on ever-smaller angular scales. (See the article by Charles Bennett, Michael Turner, and Martin White in PHYSICS TODAY, November 1997, page 32.)

The peaks are called acoustic because they're thought to be manifestations of sound like compressional waves in the plasma epoch that began a few minutes after the Big Bang and its inflationary encore. The microwave telescopes make sensitive CMB temperature maps of patches of sky, which are then fitted by a spherical-harmonic series. The power spectrum is essentially a plot of the spherical-harmonic coefficients squared, displayed as a function of l, the multipole order. The square of the l th coefficient measures the mean square spatial temperature fluctuation (or variance) at angular separations near 180 deg/l.

Last year's Boomerang and Maxima results had shown hints of a second peak. But it seemed to be lower than the theoretical expectation--if it was there at all. A lower-than-expected second acoustic peak implied one of two possibilities, both quite unpalatable to inflation theorists: Either the primordial spectrum of density fluctuations just before inflation was far from being scale invariant; or the abundance of baryons (protons and neutrons) just after inflation was significantly greater than the theory of primordial nucleosynthesis predicts.

Now the inflationists are relieved. At the April meeting of the American Physical Society in Washington, DC, John Carlstrom (University of Chicago), leader ofthe DASI team, reported that the height of the second peak yielded a cosmic baryon density in excellent agreement with the theory of primordial nucleosynthesis. At the same session, the Boomerang group reported that an expanded analysis of the data from its 1998 flight produced essentially the same baryon-density result.2

Furthermore, both the expanded Boomerang analysis and a high-resolution reanalysis of the data from the 1998 Maxima flight3 strengthened the case for the second and third acoustic peaks. All three groups reported at the Washington meeting that the theoretical fits to their data yielded a primordial spectrum of adiabatic quantum fluctuations that had essentially no dependence on length scale. Adiabatic, in this context, means that all forms of energy and matter were perturbed to the same extent. Inflation implies a nearly scale-free spectrum of adiabatic primordial fluctuations. The microwave background comes to us directly from the moment, some 400 000 years after the Big Bang, when the cosmos first became cool enough to be transparent. So why is the size distribution of its measly parts-per-million random departures from perfect isotropy so potentially informative about the first few minutes after the Big Bang?

The inflationary scenario begins with microscopic quantum fluctuations in the energy distribution that are suddenly inflated to astronomical size at about 10-35 s after the Big Bang. In the next three minutes, as the cosmos cools, the lightest nuclear species--mostly hydrogen and helium--condense out of the primordial soup of quarks, photons, and leptons. The ordinary nuclear matter is presumed to be overwhelmed by about seven times as much nonbaryonic "dark matter" of a kind we don't know about. Nonetheless, the baryonic matter plays a central role in the fully ionized hot plasma that renders the cosmos opaque for the next 400 000 years. Around the random local islands of atypically high mass density, gravity tends to accumulate still more matter. But as the local density increases, the gravitational attraction is increasingly opposed by repulsive radiation pressure. This interplay of attractive and repulsive stresses generates compressional acoustic waves in the plasma, with "sound" velocity somewhat less than c/[square root of three]. Because the nonbaryonic matter is impervious to radiation pressure, the sound-wave amplitudes depend sensitively on the baryon density.

The CMB photons we now observe have been redshifted a thousandfold in the cosmic expansion since the end of the plasma epoch. But they have not suffered any significant scattering since the plasma gave way to transparent neutral gas. So they still carry the imprint of the density fluctuations as they were at the abrupt end of the plasma epoch.

The growth of a coherent region of high density (or temperature) is limited by the velocity of the compression waves. So the largest hot spots at the end of the plasma epoch were about 200 000 light-years across. That's roughly the sound velocity times the duration of the plasma epoch. The largest accumulations of minimum density (or temperature) were about half that size, because, in the time available before the plasma cleared, an acoustic wave would have traversed such a region twice, propagating first compression and then rarefaction. Similarly, a region reaching maximum compression a second time at the end of the epoch would have been traversed three times, and thus would be limited to 1/3 the diameter of the largest hot spots. So we end up, roughly speaking, with a harmonic sequence (1, 1/2, 1/3, 1/4 ...) of characteristic sizes for alternating regions of maximal compression and rarefaction that manifest themselves is small temperature fluctuations in the CMB.

These very faint spatial fluctuations about the CMB's spectacularly uniform blackbody temperature of 2.725 K are measured in microkelvins. If one maps the CMB temperature of a patch of sky with sufficient sensitivity and angular resolution, the spherical-harmonic power spectrum should exhibit the first few acoustic peaks. One important condition for the appearance of distinct peaks in the fluctuation power spectrum is the crisp, well-defined starting time inflation imposes on the plasma epoch. The oscillations all begin almost simultaneously.

The position of the first peak tells us that the biggest CMB hot spots subtend an angle of about 1 deg on the sky. That's what one would expect at the end of the plasma epoch, if the subsequent 10¹⁰-year journey of the CMB photons was not distorted by large-scale cosmic curvature. In other words, the geometry of the universe is, as far as we can tell, quite flat.

But that was last year's news. This time, the second peak has center stage. Its height, relative to the first peak, is a sensitive measure of the baryon density in the plasma. The second peak, and in fact all the cold-spot peaks (4th, 6th,. ..), should become higher, relative to the hot-spot peaks, with decreasing baryon density. The best fits to the DASI and Boomerang power spectra both yield[omega]_b = 0.042 ± 0.008, where [omega]_b is the cosmic baryon mass density expressed as a fraction of the total "critical density" of mass and energy required to make the cosmic geometry flat. (The error quoted here ignores the uncertainty in our knowledge of the Hubble constant.)

That's in very good agreement with the [omega]_b one gets by applying the theoretical details of primordial nucleosynthesis to the most recent observations of the cosmic abundance of deuterium. It is assumed that all deuterium in the cosmos was created in the first three minutes, and the theory predicts a steep dependence of the deuterium abundance on the overall baryon density (see PHYSICS TODAY, August 1996, page 17). So here we have reassuring observational concord between the predictions of the inflationary scenario for three minutes and 400 000 years after the Big Bang.

For [omega]_m, the overall (normalized cosmic mass density for baryonic and nonbaryonic matter, a variety of different sorts of observations are convincingly converging on a value of about 0.35. In other words, the ordinary matter we know about accounts for little more than 10% of all matter. This affront to our material dignity is compounded by the growing evidence that matter as a whole plays second fiddle to some sort of dark energy ([omega]_^ is approximately 0.65). (See PHYSICS TODAY, June 2001, page 17.) The flat cosmic geometry demanded by inflation requires that [omega]_T = [omega]_m = 1. The CMB observations are particularly sensitive to this sum. The best fits to the DASI and Boomerang power spectra yield [omega]_T = 1.04 ± 0.06 and 1.02 ± 0.06, respectively.

Unlike Boomerang and Maxima, which are imaging telescopes, DASI is an interferometer that measures spherical-harmonic (or Fourier) components of the CMB directly, without having to rely on spatial images. This obviates a number of calibration problems that burden the analysis of the imaging-telescope data. The DASI design owes much to decades of successful interferometric radio astronomy. But the radio telescopes need very long baselines to achieve subarcsecond angular resolution. DASI, by contrast, can make do with baselines on the order of a meter to achieve the modest 0.2 deg resolution needed to measure the CMB power spectrum out to 1 = 900.

DASI's faceplate sports 13 microwave detectors, each with a 20-cm aperture. Pairing these detectors provides 78 interferometric baselines of 26 different lengths. Being just half a mile from the South Pole, DASI can fix its gaze continually on a patch of sky simply by rotating diurnally about its vertical axis. As Carlstrom puts it, "The Earth rotates, but we don't."

In recent weeks, galaxy redshift survey teams have reported hints of the CMB acoustic peaks in the cosmic distribution of galaxies. That's not surprising if one assumes, as cosmologists do, that the parts-per-million CMB fluctuations in the incredibly homogeneous plasma epoch were the seeds of today's highly structured universe.

As of this writing, NASA's MAP (Microwave Anisotropy Probe) satellite was scheduled for launch at the end of June. Frorn its quasi-stable perch at the Lagrange point L2, a million miles antisunward from Earth, MAP should be able to measure the CMB power spectrum with unprecedented sensitivity and precision.

1. C. Pryke et al., http://arXiv.org/abs/astro-ph/0104490.
2. P. de Bemardis et al., http://arXiv.org/abs/astro-ph/0105296.
3 R. Stompor et al., http://arXiv.org/abs/astro-ph/0105062.
4. J. O'Meara et a\..,Astrophys. J. 552,718 (2001).
5. W. J. Percival et al., http://arXiv.org/abs/astro-ph/0105252.

Do you know if this instrument has been launched yet, and when it is scheduled to start producing useful data?

Launched successfully and should reach L2 and start data collecting at the end of the month. It'll take nine months to get a complete full sky survey. MAP will be real good for temperature sensitivity, but only mediocre when compared to Maxima and Boomerang for angular resolution.

To my eye, the chi-squared per degree of freedom seems considerably less than one.

That's my favorite pick-up line ;-)

Excellent.

Thanx.

Thanks for the heads up. This is good stuff. I should be keeping on my cosmology more, that is for sure.

We're counting on folks such as yourself, "RadioAstronomer," and "Physicist" to explain the details of things like Inflationary Cosmology to the "man in the street" who wanders into these threads from time to time. I'll field the simpler question or two from time to time, but I leave the "heavy lifting" to you guys.

We're are just glad that folks like you drop in occasionally; it is a tremendous resource the FR readers to have you guys around.

7 - thanks for the physics for the ignorant explaination. You saved a lot of questions.

You're most welcome. I wasn't sure if my response would answer your questions, or just create a whole new set of questions. I defer to the really knowledgeable guys like "Physicist," "RadioAstronomer," and "ThinkPlease" on the really deep, detailed, or complex issues.

That said, I hope you were paying close attention; there'll be a pop-quiz next period!

I'll have to think about that for a bit.

I'll try to dig up the paper itself; I'm sure it will say what the chi-squared actually is.

I base my estimate on the expectation that, if the errors are correctly estimated, somewhat more than a third of the data points will be more than one sigma away from the curve. In the above plot, only three or four data points are so aberrant out of 20.

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.