The power spectrum in a strongly inhomogeneous Universe

Abstract

A crucial issue in cosmology is the determination of the fluctuation power spectrum.The standard picture of the matter clustering, the Cold Dark Matter model (and its variant), assumes that,on scales smaller than a certain ``flattening scale'' $λ_f$, the power spectrum increases with the scale, while on much larger scales it decreases so to match the tiny fluctuations observed in the microwave background. The standard picture also assumes that, once a statistically homogeneous sample is reached, the power spectrum amplitude is fixed, and any major variation should be attributed to luminosity segregation. However, the determination of $λ_f$ and of the absolute amplitude, if any, is still matter of debate. In particular, there is no consensus on whether the turnaround has been detected or not, and on the actual importance of the luminosity segregation effect. We show that, due to the finiteness of the sample the standard analysis of self-similar (fractal) distributions yields a turnaround for scales close to the survey scale, and a systematic amplitude shift with the survey scale. We point out that both features, bending and scaling, are in agreement with recent determination of the power spectrum, in particular with the CfA2 spectrum. We remark that the standard power spectrum is not a well defined statistical tool to characterize the galaxy distribution when a homogeneity scale has not been reached. In order to perform an analysis that does not imply any a priori assumption one should study the PS of the density, rather than the PS of the density contrast.