Non-detection of a statistically anisotropic power spectrum in large-scale structure

TL;DR

This study searches for quadrupolar anisotropy in the primordial power spectrum using SDSS LRG data and finds no significant evidence for such anisotropy, placing constraints on its possible amplitude.

Contribution

It provides the first constraints on quadrupolar anisotropy in large-scale structure using SDSS data, extending previous CMB analyses.

Findings

No evidence for quadrupolar power anisotropy was detected.

Constraints on anisotropy amplitude g_* were established.

Results are consistent with an isotropic primordial power spectrum.

Abstract

We search a sample of photometric luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS) for a quadrupolar anisotropy in the primordial power spectrum, in which P(\vec{k}) is an isotropic power spectrum P(k) multiplied by a quadrupolar modulation pattern. We first place limits on the 5 coefficients of a general quadrupole anisotropy. We also consider axisymmetric quadrupoles of the form P(\vec{k}) = P(k){1 + g_*[(\hat{k}\cdot\hat{n})^2-1/3]} where \hat{n} is the axis of the anisotropy. When we force the symmetry axis \hat{n} to be in the direction (l,b)=(94 degrees,26 degrees) identified in the recent Groeneboom et al. analysis of the cosmic microwave background, we find g_*=0.006+/-0.036 (1 sigma). With uniform priors on \hat{n} and g_* we find that -0.41<g_*<+0.38 with 95% probability, with the wide range due mainly to the large uncertainty of asymmetries aligned with the Galactic Plane. In none of these three analyses do we detect evidence for quadrupolar power anisotropy in large scale structure.