Fourier Phase Analysis of SDSS Galaxies
  We present a first analysis of the clustering of SDSS galaxies using the distribution function of the sum of Fourier phases. This statistic was recently proposed by one of authors as a new method to probe phase correlations of cosmological density fields. Since the Fourier phases are statistically independent of Fourier amplitudes, the phase statistic plays a complementary role to the conventional two-point statistics of galaxy clustering. In particular, we focus on the distribution functions of phase sum over three closed wavevectors as a function of the configurations of triangle wavevectors. We find that the observed distribution functions of phase sum are in good agreement with the lowest-order approximation from perturbation theory. For direct comparison with observations, we construct mock catalogs from N-body simulations taking account of several observational effects such as the survey geometry, the redshift distortion, and the discreteness due to the limited number of data. Indeed the observed phase correlations for the galaxies in the range of absolute magnitude -22<Mr<-18 agree well with those for Lambda CDM predictions with sigma8=0.9 evolved from Gaussian initial condition. This agreement implies that the galaxy biasing is approximately linear in redshift space. Instead, assuming that the galaxy biasing is described by a quadratic deterministic function at scale larger than 30Mpc/h, we can constrain the ratio of the quadratic biasing parameter b2 to the linear biasing parameter b1. We find that resulting b2/b1 is mainly dependent on sigma8 and that it is well fitted by b2/b1=0.54(+-0.06)-0.62(+-0.08)sigma8 in CDM models. Indeed, b2/b1 is nearly zero when sigma8=0.9. 
Chiaki Hikage, Takahiko Matsubara, Yasushi Suto, Changbom Park,   Alexander S. Szalay and Jon Brinkmann