A Topological Analysis of Large Scale Structure Studied Using the CMASS Sample of SDSS-III

Abstract

In this thesis, we study the three-dimensional genus topology of large-scale structure using the northern region of the CMASS sample of BOSS from SDSS-III. To date, this is the largest volume sample for which genus topology has been studied. We study the topology at two smoothing lengths - R\(_{G}\) = 21 h\(^{-1}\) Mpc and 34h\(^{-1}\) Mpc. The CMASS sample yields a genus curve that is broadly characteristic of one produced by Gaussian random-phase initial conditions. The data thus supports the standard model of inflation where random quantum fluctuations in the early universe produced Gaussian random-phase initial conditions. On top of a Gaussian random phase genus, we note some detectable deviations. First, we observe a small negative shift \(\Delta\)v, which is indicative of large structures fragmenting into many isolated clusters. Additionally, we observe A\(_{V}\) < 1 and A\(_{C}\) > 1, which indicates that the universe is made up of fewer, yet larger (more connected) voids, and more numerous, but smaller (fragmented) high density regions. These deviations from random phase occur as a result of nonlinear gravitational effects and biasing related to galaxy formation. We also find good agreement with the topological analysis of LRGs presented in Gott, et. al. (2009). However, the genus amplitude at both smoothing lengths is lower than the results of Gott, et. al. (2009) and the amplitude predicted by linear evolution using the Planck and WMAP parameters. For comparison, we also study the topology of 27 mock sky surveys constructed from the Horizon Run 3 simulation (Kim, Park, Rossi, Lee, and Gott 2011). For the most part, the simulation does an excellent job of reproducing the genus topology of the observed sample, and we detect no variation at the 2\(\sigma\) level.