CMB POWER SPECTRUM

Acoustic oscillations in the early universe — the cosmic standard ruler

0.049
0.270
0.965
The CMB angular power spectrum C_ℓ encodes the temperature fluctuations on the sky at angular scale ~180°/ℓ. Before recombination, photons and baryons formed a tightly coupled fluid; density perturbations set up acoustic oscillations — sound waves in the plasma. At recombination (~380,000 yr), these waves froze, imprinting a series of acoustic peaks whose positions depend on the sound horizon d_s ≈ 147 Mpc. The first peak at ℓ ≈ 220 corresponds to modes that completed exactly half an oscillation. The ratio of odd to even peaks constrains baryon density; the peak locations constrain spatial curvature and dark energy.