CMB Power Spectrum
The cosmic microwave background is the universe at age 380,000 years — photons released when the plasma cooled enough for atoms to form. Its temperature varies by ~10⁻⁵ across the sky. Decompose those variations into spherical harmonic modes and plot the power at each scale ℓ. Three acoustic peaks appear at ℓ ≈ 220, 540, 800 — the resonances of sound waves frozen at recombination. The peak positions pin down the universe's geometry, dark matter density, baryon content, and age.
why three peaks
Before recombination (~380,000 years after the Big Bang), the universe was a hot ionized plasma. Photons and electrons scattered constantly; the medium acted as a single fluid. Tiny density fluctuations triggered acoustic oscillations: gravitational pull collapses overdensities, photon pressure pushes back, plasma rings like a struck bell.
Different wavelengths oscillate at different frequencies — proportional to ω ∝ k for a relativistic fluid. At recombination, the photon-electron coupling dropped abruptly. Each wavelength was frozen at whatever phase of oscillation it happened to be at — and we observe that phase imprinted on the photon temperature today.
Peaks correspond to wavelengths caught at maximum compression or maximum rarefaction:
• First peak (ℓ ≈ 220): the fundamental tone — modes just reaching their first compression maximum. The peak's angular position measures the curvature of space and pins Ω_k = 0 (the universe is flat to ~0.4%).
• Second peak (ℓ ≈ 540): modes at first rarefaction. The ratio of peak heights measures baryon density: more baryons → asymmetric peaks (compression deeper than rarefaction, since baryons fall in but don't push back as hard).
• Third peak (ℓ ≈ 800): modes at second compression. The peak height relative to first measures dark matter — CDM gravitates but doesn't oscillate, providing a constant "background" potential that boosts even-numbered peaks.
This single curve, measured by COBE (1990), WMAP (2003), and Planck (2013), determines essentially every cosmological parameter we know with %-level precision. The fact that it agrees with predictions from inflation + cold dark matter + dark energy across 6 orders of magnitude in ℓ is the strongest evidence we have for the standard cosmological model.