Astronomy & Celestial Mechanics
the sky, computed
Concept

Acoustic peaks — where it appears

The regularly spaced maxima in the microwave background's angular power spectrum, left by sound waves in the early plasma caught at different phases. Their positions measure the sound horizon against the distance to last scattering, and their relative heights weigh the baryons and the dark matter.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The acoustic peaks, and where the geometry says they should be. The temperature angular power spectrum of the microwave background. The drawn curve is a monotone interpolation through the published positions and heights of the six peaks and five troughs of the Planck 2018 TT measurement — it is a representation of data, and nothing between two extrema is claimed. The marks along the top are not: they are computed from this collection's own cosmology as ℓₐ(m − 0.267), where ℓₐ = π × 13866 / 144.43 = 301.6 — π times the comoving distance to last scattering divided by the sound horizon there — is the angle the sound horizon subtends at last scattering turned into a multipole. The two agree to 2.8 per cent at worst across six peaks, which is the whole of what makes this a measurement of geometry: a wave of known physical wavelength, seen at a known distance, is a protractor. The first peak at ℓ = 220 corresponds to about 0.82 degrees on the sky — roughly twice the width of the full Moon, which is the largest hot and cold patch the sky has.

A standing wave frozen at one instant

The temperature of the microwave background varies across the sky by one part in a hundred thousand, and the sizes of the patches are not random. There is a preferred angular scale near one degree, and it is a sound wave that stopped ringing four hundred thousand years after the beginning.

cosmology · Microwave background A clumped plasma recombines earlier. The fraction of hydrogen still ionised against redshift, decreasing to the right, on a logarithmic axis, from Peebles's three-level atom: for a smooth plasma (solid), and for one whose baryons are clumped into two equal volumes at 1.71 and 0.29 times the mean density, a clumping factor of 0.5 (thick dashed, averaged by mass; thin dashed, each zone alone). Recombination goes as the density squared, so the dense zone recombines first and carries most of the mass; the average ionisation falls through one half at redshift 1292 instead of 1273, and at redshift 1100 it is 0.123 against 0.145. The photons cannot see the individual patches, which are smaller than their mean free path; they see only the average, and the average recombines earlier.

A field that would have moved the ruler

A magnetic field left over from the early universe, too weak to matter to any galaxy, could still have pushed the baryons into small clumps before the universe became transparent. Clumped hydrogen recombines earlier, the sound waves in the plasma stop sooner, and the ruler that the microwave background is read with comes out shorter — which raises the Hubble constant the background implies, in the direction of the disagreement that has resisted every other explanation.

cosmology · Primordial fields The polarisation peaks sit in the temperature troughs. A tight-coupling sketch of the two acoustic sources against multipole, each scaled to its own maximum: the temperature, from the compression of the photon–baryon fluid at last scattering plus its Doppler term, and the E-mode polarisation, which is driven by the fluid's velocity gradient. The sound horizon and the distance to last scattering put the acoustic scale at ℓ = 302, the measured phase of the peaks is 0.267 and the damping scale is ℓ = 1400; the baryons' weight, which changes the heights of the temperature peaks and not their places, is left out. The temperature peaks fall at ℓ ≈ 218, 515, 813, 1110, 1408; the polarisation peaks at ℓ ≈ 130, 391, 681, 975, 1272, between them, because a compression is at its extreme when the fluid is momentarily still, and the velocity is largest a quarter of a cycle later. The model has no projection, no decaying potentials and no thickness, so it places the peaks and says nothing about their shapes.

Polarised only where the glow was lopsided

An electron bathed in light from every side scatters it unpolarised, and so does one bathed in light brighter on one side. Only a glow brighter along one axis than across it leaves a polarisation behind, and in the microwave background that glow existed for a short time, in a thin part of a thin shell, because the plasma was moving.

cosmology · Microwave background

Named alongside it

The objects these essays reach for when they reach for this one.

Sound horizonVisibility functionAngular power spectrumBaryon clumpingBaryon loadingE mode polarisationHubble tensionLast scatteringLast scattering surfaceMagnetogenesisMean free pathMultipole

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