Field Note: The Acoustic Peaks

Baryon Oscations Frozen in the Cosmic Microwave Background

The CMB temperature power spectrum is a graph of variance versus angular scale. At first glance, it looks like noise — a jagged line rising, falling, and tapering off. But within that jagged line are peaks. Distinct, well-defined acoustic peaks that encode the physical conditions of the universe at the moment of last scattering. These peaks are the frozen remnants of sound waves that propagated through the primordial plasma before the universe became transparent.

When physicists first predicted these peaks in the late 1990s, they were a theoretical curiosity. In 1997, the BOOMERanG and MAXIMA balloon experiments detected the first peak. Since then, WMAP, Planck, and numerous ground-based experiments have measured the full spectrum with increasing precision. The peaks are real. They are the clearest evidence we have that the early universe was governed by well-understood physics — fluid dynamics and gravity, operating on cosmic scales.

The Physics

The acoustic oscillations arose from the competition between two forces. Gravity pulled matter — ordinary baryons and dark matter — together. Radiation pressure from the photon-baryon plasma pushed outward. The result was a standing wave, a compression-rarefaction cycle playing out across the universe.

Dark matter provided the gravitational wells. It did not interact with photons, so it clumped first, creating regions of enhanced gravity. Ordinary matter (baryons) and photons, which were tightly coupled through Thomson scattering, fell into these wells. But as the baryon-photon fluid compressed, radiation pressure built up and eventually overcame gravity, driving the fluid outward. The fluid expanded, cooled, and then gravity pulled it back in again. The cycle repeated.

The speed of sound in this plasma was about fifty-seven percent of the speed of light. In the 380,000 years before recombination, a sound wave could travel a maximum comoving distance of roughly one hundred and forty megaparsecs — the sound horizon. This maximum travel distance sets the physical scale of the peaks. When we project that scale onto the sky, it appears as a specific angular scale — roughly one degree — where the first acoustic peak is located.

The Peaks Themselves

The first peak corresponds to modes that have undergone exactly one compression since the onset of the oscillations. These regions are at maximum density and minimum velocity potential. They appear as hot spots in the CMB because the compressed plasma was denser and therefore hotter.

The second peak corresponds to modes that have completed one full cycle — compression, rarefaction, and then compression again. But here's something important: baryons preferentially fall into the gravitational wells, enhancing the compressions relative to the rarefactions. This means the odd-numbered peaks (compressions) are systematically higher than the even-numbered peaks (rarefactions). The ratio of the second peak amplitude to the first peak amplitude is exquisitely sensitive to the baryon density. Measurements of this ratio give us an independent determination of the baryon density that agrees beautifully with Big Bang nucleosynthesis predictions.

The third peak is the next compression mode. Its amplitude relative to the first peak tells us about the dark matter density. More dark matter means deeper gravitational wells, which drive stronger oscillations and higher peak amplitudes.

Each subsequent peak is lower in amplitude than the last. This damping — known as Silk damping, after Joseph Silk who first calculated it — occurs because photons can diffuse out of overdense regions, smoothing out the temperature fluctuations at small scales. The damping scale is sensitive to the details of the recombination process itself.

What the Spectrum Tells Us

The positions of the peaks tell us the geometry of the universe. In a flat universe, sound waves of comoving size r_s appear at angular scale θ = r_s / d_A, where d_A is the angular diameter distance to last scattering. The first peak is observed at multipole ℓ ≈ 220, corresponding to an angular scale of about one degree. This is precisely what you expect for a flat universe. A closed universe would show peaks at larger angular scales; an open universe at smaller scales. The data strongly favor flatness.

The overall shape of the spectrum — the peak locations, the relative amplitudes, the damping tail — provides a complete picture of the early universe's contents and dynamics. From it, we extract the cosmological parameters with precision that would have been unthinkable thirty years ago.