Cosmic Microwave Background
Measuring the Relic Glow of the Early Universe
The cosmic microwave background was discovered by accident in 1964 by Penzias and Wilson, who found an irreducible 3.5 K excess antenna temperature in a horn-reflector antenna at 4.08 GHz that persisted in every direction of the sky regardless of season or pointing. That isotropic signal turned out to be thermal radiation from the surface of last scattering, the moment the universe became transparent. The FIRAS instrument aboard COBE later confirmed the spectrum to be a blackbody to better than one part in 10,000, fixing the temperature at 2.72548 ± 0.00057 K and earning a Nobel Prize. From an RF engineering standpoint, the CMB is the most precisely characterized natural noise source we have, which makes it both a scientific target and a convenient absolute calibration reference for radiometers.
Because the spectral peak near 160 GHz sits above most atmospheric transmission windows, ground-based instruments observe in discrete bands at 30, 40, 90, 150, and 220 GHz, chosen to thread between the water-vapor and oxygen emission lines. Foreground contamination from galactic synchrotron radiation dominates below about 70 GHz while thermal dust emission dominates above 150 GHz, so the CMB is cleanest in the 70 to 100 GHz minimum. Separating the relic signal from these foregrounds is a multi-frequency problem, which is why modern surveys deploy detector arrays spanning the full millimeter band rather than a single channel.
The Blackbody Spectrum and Anisotropy
The CMB intensity follows the Planck blackbody law, and its frequency peak is set by Wien's displacement law. The angular power spectrum of the temperature anisotropies, decomposed into spherical harmonics, exhibits a first acoustic peak near multipole l ≈ 220, corresponding to about a 1 degree angular scale on the sky. The amplitude and positions of these acoustic peaks constrain the geometry and matter content of the universe, which is why microKelvin-level radiometric precision translates directly into cosmological measurement.
Bν(T) = (2hν3 / c2) × 1 / (ehν/kT − 1) W·m−2·sr−1·Hz−1
Spectral peak (Wien, frequency form):
νpeak ≈ 2.821 × kT / h ≈ 58.79 × T GHz/K → 160.2 GHz at 2.725 K
Radiometer sensitivity:
ΔTmin = Tsys / √(B × τ)
Where h = Planck constant, k = Boltzmann constant, c = speed of light, ν = frequency, T = physical temperature, Tsys = system noise temperature, B = RF bandwidth, τ = integration time. Example: Tsys = 10 K, B = 20 GHz, τ = 5000 s → ΔTmin ≈ 1 μK.
CMB Observing Bands and Instruments
| Band (GHz) | Wavelength | Dominant Use | Main Foreground | Detector Type |
|---|---|---|---|---|
| 30 | 10 mm | Synchrotron monitor | Galactic synchrotron | HEMT radiometer |
| 40 | 7.5 mm | Low-freq anchor | Synchrotron, free-free | HEMT radiometer |
| 90 | 3.3 mm | CMB minimum | Minimal foreground | TES bolometer |
| 150 | 2.0 mm | Primary CMB band | Onset of dust | TES bolometer |
| 220 | 1.4 mm | Dust monitor | Thermal dust | TES bolometer |
| 353 | 0.85 mm | Dust template | Thermal dust | TES bolometer |
Frequently Asked Questions
At what frequency does the cosmic microwave background spectrum peak?
As a 2.725 K blackbody, its spectral radiance peaks near 160.2 GHz (about 1.87 mm), from νpeak ≈ 2.821 kT/h ≈ 58.79 GHz/K × 2.725 K. Ground and balloon experiments observe in atmospheric windows at 30, 40, 90, 150, and 220 GHz, mostly straddling the peak; satellites like COBE, WMAP, and Planck observe through and above it from above the atmosphere.
Why must CMB radiometers be cooled to cryogenic temperatures?
Anisotropies are only tens of μK against a 2.725 K mean, so the receiver must add minimal noise. Tsys adds directly to antenna temperature, and a 300 K amplifier would swamp the signal. Cooling the front-end LNA and feed to 4 to 20 K drops amplifier noise to a few kelvin; TES bolometers run below 0.3 K. Lower physical temperature also cuts thermal emission from optics and feed horns that would contaminate the sky temperature.
How long must a radiometer integrate to detect microKelvin CMB anisotropies?
From ΔT = Tsys/√(Bτ), a coherent receiver with Tsys ≈ 10 K and 20 GHz bandwidth needs roughly 5,000 s per beam to reach 1 μK. Mapping the full sky to that depth over millions of pixels drives multi-year missions and arrays of hundreds to thousands of detectors. Bolometer arrays trade coherent gain for photon-noise-limited sensitivity and far larger pixel counts.