← 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.
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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.
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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].
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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
The same 3-kelvin glow.
CH.08 / 08 — REFERENCES