Title: 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 $2\sigma$
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.