Observational Matter Power Spectrum and the Height of the Second Acoustic Peak

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Abstract
We show that the amplitude of the second acoustic peak in the newly released BOOMERANG-98 and MAXIMA-I data is compatible with the standard primordial nucleosynthesis and with the locally broken scale-invariant matter power spectrum suggested by recent measurements of the power spectrum in the range 20-200 h-1 Mpc. If the slope of matter density perturbations on large scales is n ≈ 1, the Hubble constant is 0.5 < h < 0.75, and rms mass fluctuations at 8 h-1 Mpc are 0.65 ≤ σ8 ≤ 0.75, then for a universe approximately 14 Gyr old, our best fit within the nucleosynthesis bound ΩBh2 = 0.019 ± 0.0024 requires 0.3 ≤ Ωm ≤ 0.5. Cluster abundances further constrain the matter density to be Ωm ≈ 0.3. The CMB data alone are not able to determine the detailed form of the matter power spectrum in the range 0.03 < k < 0.06 h Mpc-1, in which deviations from the scale-invariant spectrum are expected to be most significant, but they do not contradict the existence of the previously claimed peak at k ~ 0.05 h Mpc-1 and a depression at k ~ 0.035 h Mpc-1.