First-year Wilkinson microwave anisotropy probe (WMAP) observations: Interpretation of the TT and TE angular power spectrum peaks

The CMB has distinct peaks in both its temperature angular power spectrum (TT) and temperature-polarization cross-power spectrum (TE). From the WMAP data we find the first peak in the temperature spectrum at ℓ = 220.1 ± 0. 8 with an amplitude of 74.7 ± 0.5 μK; the first trough at ℓ = 411.7 ± 3.5 with an amplitude of 41.0 ± 0.5 μK; and the second peak at ℓ = 546 ± 10 with an amplitude of 48.8 ± 0.9 μK. The TE spectrum has an antipeak at ℓ = 137 ± 9 with a cross-power of -35 ± 9 μK², and a peak at ℓ = 329 ± 19 with cross-power 105 ± 18 μK². All uncertainties are 1 σ and include calibration and beam errors. An intuition for how the data determine the cosmological parameters may be gained by limiting one's attention to a subset of parameters and their effects on the peak characteristics. We interpret the peaks in the context of a flat adiabatic ΛCDM model with the goal of showing how the cosmic baryon density, Ω_bh ², matter density, Ω_mh², scalar index, n_s, and age of the universe are encoded in their positions and amplitudes. To this end, we introduce a new scaling relation for the TE antipeak-to-peak amplitude ratio and recompute known related scaling relations for the TT spectrum in light of the WMAP data. From the scaling relations, we show that WMAP's tight bound on Ω_bh² is intimately linked to its robust detection of the first and second peaks of the TT spectrum.