2010/10/31 by Xin Wang, Xuelei Chen, Changbom Park · 21 citations
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Galaxy #Genus #Gravitation #Measure (data warehouse) #Redshift #Relativity and Gravitational Theory #Scale (ratio) #Sensitivity (control systems) #Topology (electrical circuits) #astro-ph.CO #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0004-637x/747/1/48
published in The Astrophysical Journal 747(1), 48 (IOP Publishing) · Introduction and discussion expanded and refined, conclusion unchanged, 10 pages, 8 figures. ApJ accepted
arxiv created 2011/12/18 · openalex publication_date 2012/02/13 · arxiv updated 2015/05/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The genus of the isodensity contours is a robust measure of the topology of a large-scale structure, and it is relatively insensitive to nonlinear gravitational evolution, galaxy bias, and redshift-space distortion. We show that the growth of density fluctuations is scale dependent even in the linear regime in some modified gravity theories, which opens a new possibility of testing the theories observationally. We propose to use the genus of the isodensity contours, an intrinsic measure of the topology of the large-scale structure, as a statistic to be used in such tests. In Einstein's general theory of relativity, density fluctuations grow at the same rate on all scales in the linear regime, and the genus per comoving volume is almost conserved as structures grow homologously, so we expect that the genus–smoothing-scale relation is basically time independent. However, in some modified gravity models where structures grow with different rates on different scales, the genus–smoothing-scale relation should change over time. This can be used to test the gravity models with large-scale structure observations. We study the cases of the theory, DGP braneworld theory as well as the parameterized post-Friedmann models. We also forecast how the modified gravity models can be constrained with optical/IR or redshifted 21 cm radio surveys in the near future.