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

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 $2σ$ 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.