# Limits on statistical anisotropy from BOSS DR12 galaxies using bipolar spherical harmonics

## TL;DR

This study uses bipolar spherical harmonics to analyze galaxy clustering data from BOSS DR12, constraining primordial anisotropy parameters and finding no significant evidence for statistical anisotropy.

## Contribution

It introduces a method to measure and correct for survey geometry contamination in anisotropy analysis using BipoSHs, providing the first tight constraints on primordial anisotropy parameters from galaxy data.

## Key findings

- No significant anisotropy detected within 2σ level.
- Constraints on primordial anisotropy parameter g_*: -0.09 to 0.08.
- Method effectively accounts for survey geometry effects.

## Abstract

We measure statistically anisotropic signatures imprinted in three-dimensional galaxy clustering using bipolar spherical harmonics (BipoSHs) in both Fourier space and configuration space. We then constrain a well-known quadrupolar anisotropy parameter $g_{2M}$ in the primordial power spectrum, parametrized by $P(\vec{k}) = \bar{P}(k) [ 1 + \sum_{M} g_{2M} Y_{2M}(\hat{k}) ]$, with $M$ determining the direction of the anisotropy. Such an anisotropic signal is easily contaminated by artificial asymmetries due to specific survey geometry. We precisely estimate the contaminated signal and finally subtract it from the data. Using the galaxy samples obtained by the Baryon Oscillation Spectroscopic Survey Data Release 12, we find no evidence for violation of statistical isotropy, $g_{2M}$ for all $M$ to be of zero within the $2\sigma$ level. The $g_{2M}$-type anisotropy can originate from the primordial curvature power spectrum involving a directional-dependent modulation $g_* (\hat{k} \cdot \hat{p})^2$. The bound on $g_{2M}$ is translated into $g_*$ as $-0.09 < g_* < 0.08$ with a $95\%$ confidence level when $\hat{p}$ is marginalized over.