We describe an attempt to reconstruct the initial conditions for the formation of cosmological large-scale structure , under the assumption of gravitational instability in a Gaussian density field .
Information on the power spectrum of the primordial fluctuations is provided by a variety of autocorrelation and cross-correlation analyses on samples of different classes of galaxy and galaxy clusters .
These results differ from the desired linear power spectrum because of three modifying effects : bias , nonlinear evolution and redshift-space distortions .
We show how the latter two effects can be corrected for analytically , allowing the linear mass spectrum to be recovered provided the bias is independent of scale for a given class of galaxy .
We argue that this is a good assumption for large scales , which is well verified in practice .

We apply this method to eight independent datasets , and obtain excellent agreement in the estimated linear power spectra for wavelengths \lambda \mathrel { \raise 1.16 pt \hbox { $ > $ } \kern - 7.0 pt \lower 3.06 pt \hbox { { $% \scriptstyle \sim$ } } } 10 h ^ { -1 } Mpc , given the following conditions .
First , the relative bias factors for Abell clusters , radio galaxies , optical galaxies and IRAS galaxies must be in the ratios b _ { \scriptscriptstyle A } :b _ { \scriptscriptstyle R } :b _ { % \scriptscriptstyle O } :b _ { \scriptscriptstyle I } = 4.5 : 1.9 : 1.3 : 1 , to within 6 per cent rms .
Second , the data require a significant degree of redshift-space distortion : \Omega ^ { 0.6 } / b _ { \scriptscriptstyle I } = 1.0 \pm 0.2 .
Third , low values of \Omega and bias are disfavoured because nonlinear evolution would spoil the agreement in shape between galaxy and cluster power spectra .
The amplitude of the preferred linear power spectrum is only weakly dependent on \Omega and agrees well at large wavelengths with the normalization demanded by the COBE data for a scale-invariant primordial spectrum , provided \Omega = 1 and gravity-wave anisotropies are negligible .
In this case , the shape of the spectrum is extremely well described by a CDM transfer function with an apparent value of the fitting parameter \Omega h = 0.25 .
Tilted models , for which inflation requires a large gravity-wave contribution to the COBE data , predict too little power at 100 Mpc wavelengths .