Polypolar spherical harmonic decomposition of galaxy correlators in redshift space: Toward testing cosmic rotational symmetry

TL;DR

This paper introduces a novel spherical harmonic decomposition method to detect and distinguish potential violations of cosmic rotational symmetry in galaxy correlation data, enhancing the ability to test fundamental cosmological assumptions.

Contribution

The authors develop a polypolar spherical harmonic decomposition technique that isolates symmetry-breaking signals in galaxy correlators, enabling model-independent tests of rotational invariance.

Findings

Nonzero L=1 and L=2 modes indicate dipolar and quadrupolar symmetry breakings.

Forecasts suggest current surveys can detect symmetry violations at Planck sensitivity levels.

Method is applicable to various anisotropic fluctuation searches in cosmology.

Abstract

We propose an efficient way to test rotational invariance in the cosmological perturbations by use of galaxy correlation functions. In symmetry-breaking cases, the galaxy power spectrum can have extra angular dependence in addition to the usual one due to the redshift-space distortion, $ \hat{k} \cdot \hat{n}$. We confirm that, via the decomposition into not the usual Legendre basis ${\cal L}_\ell(\hat{k} \cdot \hat{n})$ but the bipolar spherical harmonic one $\{Y_{\ell}(\hat{k}) \otimes Y_{\ell'}(\hat{n})\}_{LM}$, the symmetry-breaking signal can be completely distinguished from the usual isotropic one since the former yields nonvanishing $L \geq 1$ modes but the latter is confined to the $L = 0$ one. As a demonstration, we analyze the signatures due to primordial-origin symmetry breakings such as the well-known quadrupolar-type and dipolar-type power asymmetries and find nonzero $L = 2$ and $1$ modes, respectively. Fisher matrix forecasts of their constraints indicate that the $Planck$-level sensitivity could be achieved by the SDSS or BOSS-CMASS data, and an order-of-magnitude improvement is expected in a near future survey as PFS or Euclid by virtue of an increase in accessible Fourier mode. Our methodology is model-independent and hence applicable to the searches for various types of statistically anisotropic fluctuations.