In this paper we evaluate the spectrum of the pregalactic density field on scales 1 h ^ { -1 } { Mpc } < r < 100 h ^ { -1 } Mpc from a variety of astronomical data .
We start with the APM data on the projected angular correlation function , w ( \theta ) , in six narrow magnitude bins and check whether possible evolutionary effects can affect inversion of the w ( \theta ) data in terms of the underlying power spectrum .
This is done by normalizing to the angular correlation function on small scales where the underlying 3-dimensional galaxy correlation function , \xi ( r ) , is known .
Using the APM data in narrow magnitude bins allows us to test the various fits to the APM data power spectrum more accurately .
We find that for linear scales r > 10 h ^ { -1 } Mpc the Baugh and Efstathiou ( 1993 ) spectrum of galaxy distribution gives the best fit to the data at all depths .
Fitting power spectra of CDM models to the data at all depths requires \Omega h = 0.2 if the primordial index n = 1 and \Omega h = 0.3 if the spectrum is tilted with n = 0.7 .
Next 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 \Omega ^ { 0.6 } / b \simeq ( 0.2-0.4 ) .
These steps enable us to fix the pregalactic mass density field on scales between 10 and \sim 100 h ^ { -1 } Mpc .
The next dataset we use to determine the pregalactic density field 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 no CDM model can fit all the three datasets : APM data on w ( \theta ) , the data on cluster correlation function , and the data on the latter ’ s amplitude-richness dependence .
Next 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 coincide , fixes the value of \Omega to be 0.3 in agreement with observations of the dynamics of the Coma cluster .
We then use the data on high- z objects to constrain the small-scale part , ( 1-5 ) h ^ { -1 } Mpc of the pregalactic density field .
We argue that the data at high redshifts require more power than given by CDM models normalized to the APM and cluster data .
Then we reconstruct the pregalactic density field out of which modern-day galaxies have formed .
We use the data on blue absolute luminosities , the fundamental plane relations and the latest X-ray data on the halo velocity dispersion .
From this we recover the pregalactic density field on comoving scales between 1 and 5 h ^ { -1 } Mpc which is in reasonable agreement with the simple power-law extrapolation from the larger scales .