Reconstructing primordial density fluctuations – I. Method

Observed large-scale structure may have developed by gravitational instability from small inhomogeneities of the early universe. This paper describes a method for recovering primordial fluctuations from the present-day galaxy distribution, on the assumption that these fluctuations were Gaussian. The key element of the method is 'Gaussianization', a monotonic transformation of the smoothed galaxy distribution, which exploits the fact that gravitational evolution and biased galaxy formation tend to preserve the rank order of the initial density field. In tests on N-body simulations with known initial conditions, the reconstruction procedure recovers accurate maps of the initial fluctuations from fully sampled, sparsely sampled, or biased data. Evolution of the reconstructed initial conditions yields credible reproductions of the input data. Reconstruction analysis can be used to derive the properties of primordial fluctuations, to constrain biased galaxy formation and the value of Ω, and to test the hypotheses of gravitational instability and Gaussian primordial fluctuations.