Important ingredients in the model are that the haloes be biased tracers of the linear power spectrum and have a uniform profile with a correlation between the internal structure and the mass which should span a wide range sampling a Press-Schechter (1974) like mass function. Many of the features of the power spectrum of density fluctuations in the Universe can be simply understood in a model based on virialized haloes. Here we see that the agreement is very good over more than two decades in length-scale. 2 compared to the same ratio from the N-body simulations. We show the prediction for the ratio of redshift-space to real-space power in Fig. The model underestimates the N-body results in Fig. This is not surprising since Sheth (1996) and Diaferio& Geller (1996) have shown that a sum of Gaussian random velocities weighted by the Press-Schechter (1974) mass function provides a good description of the exponential distribution of velocities seen in N-body simulations. The high- k behaviour of the model qualitatively reproduces the suppression seen in the N-body simulations. Since at present such prescriptions are somewhat ad hoc we shall concentrate here on the mass power spectrum, though there is no obstacle in principle to extending the method to galaxies. The extensions to this theory introduced recently allow one to calculate the power spectra and cross-correlations between both the mass and the galaxies, given a suitable prescription for how galaxies populate dark matter haloes. The model for non-linear clustering is based on the Press-Schechter (1974) theory, in which all of the mass in the Universe resides in a virialized halo of a certain mass. It is the purpose of this work to show that redshift-space distortions can be handled naturally in the halo picture and that doing so provides insight into some well-studied phenomena. The work to date has all focused on the clustering of the matter or galaxies in ‘real space’, whereas many if not most observations of clustering take place in ‘redshift space’. ![]() While this model requires many ingredients to be fixed by numerical experiments (typically N-body simulations) it provides a useful structure for thinking about gravitational clustering which gives insights into several outstanding problems ( Seljak 2000 Peacock& Smith 2000 Seljak, Burwell& Pen 2001 Atrio-Barandela& Mucket 1999 Cooray, Hu& Miralda-Escude 2000). Specifically most pairs of dark matter particles with small inter-particle separations lie within the same halo, and thus their correlations can be predicted by the halo profile. They postulate that on large scales the haloes cluster according to linear theory while on small scales the power is dominated by the halo profiles ( Neyman, Scott& Shane 1953 Peebles 1974). Recently several authors ( Ma& Fry 2000 Seljak 2001 Peacock 2000 Peacock& Smith 2000) have developed a new way of looking at the non-linear power spectrum which imagines all the mass in the Universe lies in a halo of some mass ( Press& Schechter 1974). While the theory behind the power spectrum in the linear regime is quite straightforward, analytically handling clustering in the non-linear regime has proven quite difficult. ![]() It is robust, but sensitive to several cosmological parameters such as the Hubble constant, the matter density and of course the primordial power spectrum (usually parametrized by an amplitude and a slope). The power spectrum of the mass fluctuations in the Universe is one of the most fundamental quantities in large-scale structure. ![]() ![]() Cosmology: theory, large-scale structure of Universe 1 Introduction
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