Three-dimensional genus topology of luminous red galaxies

Abstract

We measure the three-dimensional genus topology of large-scale structure using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey and find it consistent with the Gaussian random phase initial conditions expected from the simplest scenarios of inflation. This studies three-dimensional topology on the largest scales ever obtained. The topology is spongelike. We measure topology in two volume-limited samples: a dense shallow sample studied with smoothing length of 21 h -1 Mpc, and a sparse deep sample studied with a smoothing length of 34 h -1 Mpc. The amplitude of the genus curve is measured with 4% uncertainty. Small distortions in the genus curve expected from nonlinear biasing and gravitational effects are well explained (to about 1σ accuracy) by N-body simulations using a subhalo-finding technique to locate LRGs. This suggests that the formation of LRGs is a clean problem that can be modeled well without any free-fitting parameters. This bodes well for using LRGs to measure the characteristic scales such as the baryon oscillation scale in future deep redshift surveys. © 2009. The American Astronomical Society. All rights reserved..