Cosmic Microwave Background

Discovery

In 1964, Arno Penzias and Robert Wilson at Bell Telephone Laboratories discovered the CMB while calibrating a horn antenna originally built for satellite communication at 4080 MHz (7.35 cm). They detected a persistent isotropic noise of 3.5 ± 1.0 K that could not be eliminated — no matter where they pointed the antenna. The noise was uniform in all directions and did not vary with time of day or season, ruling out solar or terrestrial origins. They received the 1978 Nobel Prize in Physics for this discovery.

Concurrently, a team at Princeton led by Robert Dicke, Jim Peebles, Peter Roll, and David Wilkinson was building a Dicke radiometer specifically to search for the CMB. Upon hearing of Penzias and Wilson's detection, Dicke famously remarked: "Boys, we've been scooped."

Physical Origin

Before recombination (z ≈ 1100), the universe was a hot, opaque plasma of protons, electrons, and photons tightly coupled via Thomson scattering. Photons had a mean free path of approximately 10 cm, constantly scattering off free electrons. The plasma acted as a blackbody at temperature T(z) = T₀(1+z), where T₀ = 2.725 K.

As the universe expanded and cooled to approximately 3000 K (at z ≈ 1100), the rate of recombination exceeded the ionization rate. Electrons combined with protons to form neutral hydrogen atoms. The photon mean free path increased from ~10 cm to the size of the observable universe in a few thousand years. These decoupled photons have been streaming freely ever since, their wavelength stretched by cosmic expansion from ~1 μm (visible/near-IR) to ~1.87 mm (microwave) by a factor of (1+z) ≈ 1100.

Spectral Characteristics

The CMB is the most perfect blackbody ever observed in nature. The FIRAS instrument on the COBE satellite (1989–1993) measured the spectrum to extraordinary precision:

• Peak frequency: 160.2 GHz (λ = 1.87 mm)
• Peak wavelength (Wien): λ_max = b/T = 2.898 × 10⁻³ / 2.725 = 1.063 mm
• Peak intensity: B_ν(T) = 2hν³/c² × 1/(e^(hν/kT) - 1) at 160.2 GHz
• Temperature precision: T₀ = 2.72548 ± 0.00057 K
• Spectral index deviation: |n - 4| < 3 × 10⁻⁵ (deviation from perfect blackbody)
• Peak spectral radiance: ~385 MJy/sr at 160.2 GHz

The Planck function for the CMB spectrum:

B_ν(T) = (2hν³/c²) × 1/(e^(hν/kT) - 1)

Where:
  h = 6.626 × 10⁻³⁴ J·s  (Planck constant)
  k = 1.381 × 10⁻²³ J/K   (Boltzmann constant)
  c = 2.998 × 10⁸ m/s     (speed of light)
  T = 2.725 K              (CMB temperature)

Peak occurs at: ν_peak = 2.82kT/h = 160.2 GHz

Anisotropies

While the CMB is remarkably uniform (isotropic to ~1 part in 100,000), tiny temperature fluctuations (anisotropies) encode the seeds of all cosmic structure. These were first detected by the COBE satellite's DMR instrument in 1992 (George Smoot and John Mather — 2006 Nobel Prize).

The angular power spectrum of CMB anisotropies (Cₗ vs. multipole moment ℓ) reveals:

• Sachs-Wolfe plateau (ℓ < 30): Primordial density fluctuations from inflation, ΔT/T ≈ 10⁻⁵
• Acoustic peaks (30 < ℓ < 1000): Sound waves in the photon-baryon plasma before recombination. First peak at ℓ ≈ 220 (angular scale ~1°) — confirms flat universe (Ω_total ≈ 1.000 ± 0.002)
• Damping tail (ℓ > 1000): Silk damping — photon diffusion washing out small-scale fluctuations

The acoustic peak positions constrain cosmological parameters:

First peak position: ℓ₁ ≈ 220
  → Angular diameter distance → Ω_k ≈ 0 (flat universe)

Peak height ratios:
  → baryon density: Ω_b h² = 0.0224 ± 0.0001
  → matter density: Ω_m h² = 0.143 ± 0.001
  → Hubble constant: H₀ = 67.4 ± 0.5 km/s/Mpc

Number of peaks observed: 8+ (Planck 2018)
Third peak height → dark matter density: Ω_c h² = 0.120 ± 0.001

Key Experiments

Penzias & Wilson Horn Antenna (1964): 6.5-meter horn antenna at Holmdel, NJ. Operated at 4080 MHz (7.35 cm). Detected T = 3.5 ± 1.0 K isotropic noise. Originally built for Project Echo and Telstar satellite communication.

COBE (1989–1993): NASA satellite carrying FIRAS (Far Infrared Absolute Spectrophotometer) and DMR (Differential Microwave Radiometer). FIRAS measured the CMB spectrum to be a perfect blackbody with T = 2.725 ± 0.002 K. DMR detected anisotropies at angular scales of 7° with ΔT/T ≈ 10⁻⁵.

WMAP (2001–2010): Wilkinson Microwave Anisotropy Probe. Mapped CMB anisotropies across the full sky at 5 frequency bands (23–94 GHz) with angular resolution 0.23°–0.93°. Established the ΛCDM cosmological model: 4.6% ordinary matter, 24% dark matter, 71.4% dark energy.

Planck (2009–2013): ESA satellite with highest-resolution CMB maps: angular resolution 5 arcminutes, frequency coverage 30–857 GHz in 9 bands. Measured 8+ acoustic peaks. T₀ = 2.7255 ± 0.0006 K. Constrained inflationary parameters and the effective number of neutrino species N_eff = 3.04 ± 0.18.

地面 experiments: BICEP/Keck (South Pole, 95/150/220 GHz), ACT (Atacama, 90/150 GHz), SPT (South Pole Telescope, 90/150/220 GHz) — measuring CMB polarization and lensing at high resolution.

Polarization

The CMB is linearly polarized at the level of ~1 μK (about 10% of the temperature anisotropy). This polarization arises from Thomson scattering of the anisotropic radiation field by free electrons at the surface of last scattering. The polarization pattern decomposes into:

• E-modes (gradient pattern): Generated by scalar (density) perturbations. Detected by DASI in 2002. Amplitude ~5 μK. Used to constrain optical depth to reionization τ ≈ 0.054 ± 0.007.
• B-modes (curl pattern): Generated by (a) gravitational lensing of E-modes (detected by SPTpol, POLARBEAR), and (b) primordial gravitational waves from inflation (not yet definitively detected). Tensor-to-scalar ratio r < 0.036 (BICEP/Keck 2021).

Cosmological Significance

The CMB is the single most important observational pillar of modern cosmology. It confirms:

• The Big Bang model — the universe was once hot and dense
• 宇宙 flatness — total density parameter Ω = 1.000 ± 0.002
• Composition — 4.6% baryonic matter, 24% dark matter, 71.4% dark energy
• Age of the universe — 13.797 ± 0.023 billion years
• Structure formation — tiny primordial density perturbations grew into galaxies and clusters
• Inflation — nearly scale-invariant spectrum of primordial perturbations (n_s = 0.965 ± 0.004)