Reconstructing the spectrum of the pregalactic density field from astronomical data

Abstract

In this paper we evaluate the spectrum of the pregalactic density field on scales $1h^{-1}Mpc < r < 100h^{-1}$Mpc from a variety of astronomical data. APM data on $w(θ)$ in six narrow magnitude is used, after correcting to possible evolutionary effects, to constrain the spectrum of galaxy clustering on scales $10h^{-1}Mpc < r < 50-100h^{-1}Mpc$. Fitting power spectra of CDM models to the data at all depths requires $Ωh=0.2$ if the primordial index $n=1$ and $Ωh=0.3$ if the spectrum is tilted with $n=0.7$. Then we compare the peculiar velocity field predicted by the APM spectrum of galaxy (light) distribution with the actual velocity data. The two fields are consistent and the comparison suggests that the bias factor is scale independent with $Ω^{0.6}/b\simeq$(0.2-0.3). The next dataset used comes from the cluster correlation data. We calculate in detail the amplification of the cluster correlation function due to gravitational clustering and use the data on both the slope of the cluster correlation function and its amplitude-richness dependence. Cluster masses are normalized using the Coma cluster. We find that CDM models are hard to reconcile with all the three datasets: APM data on $w(θ)$, the data on cluster correlation function, and the data on the latter's amplitude-richness dependence. We show that the data on the amplitude-richness dependence can be used directly to obtain the spectrum of the pregalactic density field. Applying the method to the data, we recover the density field on scales between 5 and 25$h^{-1}$Mpc whose slope is in good agreement with the APM data on the same scales. Requiring the two amplitudes to be the same, fixes the value of $Ω$ to be 0.3 in agreement with observations of the dynamics of the Coma cluster. Finally we use the data