# Super-sample tidal modes on the celestial sphere

## TL;DR

This paper introduces a bipolar spherical harmonic formalism to characterize super-sample tidal effects, demonstrating its ability to disentangle these effects from other cosmological distortions and showing they can be detected without compromising other measurements.

## Contribution

It proposes a novel BipoSH-based method to analyze super-sample tides and assesses their impact on cosmological parameter measurements using Fisher analysis.

## Key findings

- BipoSH formalism effectively breaks degeneracies among tidal, RSD, and AP effects.
- Super-sample tides have minimal impact on RSD and AP measurements.
- Super-sample tides are detectable with high accuracy in upcoming galaxy surveys.

## Abstract

The super-sample tidal effect carries information on long-wavelength fluctuations that we cannot measure directly. It arises from the mode-coupling between short-wavelength and long-wavelength perturbations beyond a finite region of a galaxy survey and violates statistical isotropy of observed galaxy power spectra. In this paper, we propose the use of bipolar spherical harmonic (BipoSH) decomposition formalism to characterize statistically anisotropic power spectra. Using the BipoSH formalism, we perform a comprehensive study of the effect of the super-sample tides on measurements of other cosmological distortions such as the redshift-space distortion (RSD) and Alcock-Paczy\'{n}ski (AP) effects by means of the Fisher information matrix formalism. We find that the BipoSH formalism can break parameter degeneracies among the super-sample tidal, RSD and AP effects, indicating that the super-sample tides have little impact on the measurements of the RSD and AP effects. We also show that the super-sample tides are detectable with an accuracy better than the $\Lambda$CDM prediction without impairing the accuracy of measurements of other anisotropies assuming a SPHEREx-like galaxy survey.