Reconstructing the Spectrum of the Pregalactic Density Field from Astronomical Data

In this paper we evaluate the spectrum of the pregalactic density field onscales $1h^{-1}Mpc < r < 100h^{-1}$Mpc from a variety of astronomical data. APMdata on $w(\theta)$ in six narrow magnitude is used, after correcting topossible evolutionary effects, to constrain the spectrum of galaxy clusteringon scales $10h^{-1}Mpc < r < 50-100h^{-1}Mpc$. Fitting power spectra of CDMmodels to the data at all depths requires $\Omega h=0.2$ if the primordialindex $n=1$ and $\Omega h=0.3$ if the spectrum is tilted with $n=0.7$. Then wecompare the peculiar velocity field predicted by the APM spectrum of galaxy(light) distribution with the actual velocity data. The two fields areconsistent and the comparison suggests that the bias factor is scaleindependent with $\Omega^{0.6}/b\simeq$(0.2-0.3). The next dataset used comesfrom the cluster correlation data. We calculate in detail the amplification ofthe cluster correlation function due to gravitational clustering and use thedata on both the slope of the cluster correlation function and itsamplitude-richness dependence. Cluster masses are normalized using the Comacluster. We find that CDM models are hard to reconcile with all the threedatasets: APM data on $w(\theta)$, the data on cluster correlation function,and the data on the latter's amplitude-richness dependence. We show that thedata on the amplitude-richness dependence can be used directly to obtain thespectrum of the pregalactic density field. Applying the method to the data, werecover the density field on scales between 5 and 25$h^{-1}$Mpc whose slope isin good agreement with the APM data on the same scales. Requiring the twoamplitudes to be the same, fixes the value of $\Omega$ to be 0.3 in agreementwith observations of the dynamics of the Coma cluster. Finally we use the dataComment: to be published in Ap.J - minor revision + typos correcte