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

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 $20 - 200$ Mpc. If the slope of matter density perturbations on large scales is $n \approx 1$, the Hubble constant is $0.5< h < 0.75$, and r.m.s. mass fluctuations at 8 Mpc are $0.65 \le \sigma_8 \le 0.75$, then for a Universe approximately 14 Gyr old our best fit within the nucleosynthesis bound $\Omega_Bh^2= 0.019 \pm 0.0024$ requires $0.3 \le \Omega_m \le 0.5$. Cluster abundances further constraint the matter density to be $\Omega_m \approx 0.3$. The CMB data alone are not able to determine the detailed form of the matter power spectrum in the range $0.03<k<0.06$ \hmpc where 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 $k\sim 0.05$ \hmpc, and a depression at $k\sim 0.035$ \hmpc.