← INDEX — FIG. 00 — 2.72548 K, EVERY DIRECTION z ≈ 1090 · 13.8 Gyr

GLOW
THE COSMIC MICROWAVE BACKGROUND

Point a radio telescope at any empty patch of sky.

BEGIN — CHAPTER 01 →

CH.01 / 08 — HOLMDEL, NEW JERSEY, 1964–65

A noise that came from everywhere

Penzias and Wilson measured about 3.5 K of excess noise [1].

Dicke's group explained it [2]; predicted earlier [19]; Nobel 1978 [3].

THE WAVELENGTH THEY LISTENED AT

λ = c / ν = 299 792 458 m/s ÷ 4.080 × 10⁹ Hz = 7.35 cm

One frequency, one temperature.

CH.02 / 08 — COBE / FIRAS, 1989–90

One temperature fits every point

FIRAS: deviations under 50 ppm [5][6].

T0 = 2.72548 K [7]; Nobel 2006 [8].

PLANCK'S LAW AND ITS PEAK

I(ν) = (2hν³/c²) / (e^(hν/kT) − 1) · ν_peak = 2.8214 kT/h · n_γ = 16πζ(3)(kT/hc)³

Units and peaks.

TEMPERATURE—

FIRAS points [5].

CH.03 / 08 — T = T₀ (1 + z)

A thermometer that runs back in time

z* = 1089.92 [11] → about 2,970 K.

About 370,000 years; age today 13.797 Gyr [11].

AGE AT REDSHIFT z (FLAT ΛCDM, PLANCK 2018)

t(z) = ∫₀^(1/(1+z)) da / (a H₀ √(Ωm a⁻³ + Ωr a⁻⁴ + ΩΛ))

Model notes.

REDSHIFT, log₁₀(1 + z)—

Presets.

CH.04 / 08 — COBE / DMR, 1992

One part in a thousand, then one in a hundred thousand

Dipole 3.362 mK from 369.82 km/s [10]; DMR [4]; RELIKT-1 [20].

30 µK, one part in 100,000 [9].

THE DOPPLER DIPOLE

T(θ) = T₀ / (γ (1 − β cos θ)) · β = v/c · ΔT ≈ T₀ β

Planck's dipole [10].

SPEED THROUGH THE BACKGROUND—

Notes.

CH.05 / 08 — COBE 7°, WMAP 13′, PLANCK 5′

Bringing the ripples into focus

WMAP: 13′, first peak at ℓ = 220.1 [12][13][14].

Planck: about 5′ [10][17].

WHAT A BEAM DOES TO EACH SCALE

B_ℓ = exp(−ℓ(ℓ+1) σ² / 2) · σ = FWHM / √(8 ln 2) · θ ≈ 180° / ℓ

Gaussian beam.

Simulated sky, not the real one.

CH.06 / 08 — PLANCK 2018

A billion pixels, six numbers

θ* to 0.03 %; 18 peaks [10][11].

Six parameters; H0 tension [10][11].

THE ACOUSTIC SCALE

θ* = r* / D_M · r* = 144.43 Mpc · 100 θ* = 1.0411 ± 0.0003 (θ* in radians)

Planck 2018 values [11].

CH.07 / 08 — LEGACY

From a hiss in a horn to a precision science

See it as an installation: Relic draws Planck's real map of this light, lets you add our motion and blur it to COBE's beam, and plays its spectrum as a chord.

The same 3-kelvin glow.

CH.08 / 08 — REFERENCES