Abstract:

The power spectrum of density fluctuations in the evolved universe provides constraints on cosmological parameters that are complementary to cosmic microwave background and other astronomical probes. The Sloan Digital Sky Survey (SDSS) Luminous Red Galaxy (LRG) sample probes a volume of ~ 3 (Gpc)3 , and systematic errors in modeling the nonlinearities limit our ability to extract information on the shape of the linear power spectrum. There are three main effects that distort the observed power spectrum from the linear power spectrum: nonlinear gravitational evolution, redshift space distortions, and a nonlinear relation between the galaxy density field and the underlying matter density field. In this thesis we introduce a new method to mitigate the latter two distortions and rely on carefully tuned N-body simulations to model the first.

In Chapter 2 we present the technique 'Counts-in-Cylinders' (CiC) and use it to measure the multiplicity function of groups of LRGs in SDSS. We use the Halo Occupation Distribution description of the galaxy-matter mapping and N -body simulations to connect this observation with constraints on the distribution of LRGs in dark matter halos. In Chapter 3 we study the effects of resolution on statistics relating to both the large and small scale distributions and motions of matter and dark matter halos. We combine these results to produce a large set of high quality mock LRG catalogs that reproduce the higher order statistics in the density field probed by the CiC technique. Using these catalogs we present a detailed analysis of the method used in Tegmark et al. (2006) to estimate the LRG power spectrum, and find that the large nonlinear correction necessary for their analysis is degenerate with changes in the linear spectrum we wish to constrain. We show that the CiC group-finding method in Chapter 2 can be used to reconstruct the underlying halo density field. The power spectrum of this field has only percent-level deviations from the underlying matter power spectrum, and will therefore provided tighter constraints on cosmological parameters. Techniques presented in this thesis will be useful for final analysis of the SDSS LRGs and upcoming surveys probing much larger volumes.