Wide-angle and relativistic effects in Fourier-space clustering statistics

Wide-angle effects in the galaxy bispectrum

“…As it can be seen from figure 3, the corrections are the order of few %'s of the flat-sky bispectrum monopole. This holds in general, for all triangular configurations and in the redshift range z ∈ [1,2]. This could have important implications for searches of new physics in the dipole of the bispectrum.…”

“…Recently, similar questions were addressed by the Authors of [1], who computed wideangle corrections the bispectrum multipoles using a Cartesian basis. In this work we will provide a different formulation of wide-angle effects, based on an expansion in spherical tensors, which is more easily adapted to the state-of-the art approaches to the convolution of the theoretical model with a survey window function [50], whose effects become important on the same scales of the wide-angle corrections.…”

“…For the power spectrum, wide-angle effects have been studied extensively [1,[55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. As the consequence of the partially broken translation invariance, the power spectrum is no longer diagonal, δ(k 1 )δ(k 2 ) = P (k 1 , k 2 ).…”

“…In principle the same technique can be applied to the bispectrum. As recently shown by [1], under the assumption of periodic boundary condition (neglecting window function effects), the wide-angle effects in the bispectrum can be described perturbatively, written schematically as follows…”

“…6 So far the relativistic effects has been included in the 3-dimensional Fourier bispectrum only within the flat-sky approximation, 7 see e.g. [75-77, 112, 113] or neglecting the convolution with a realistic window function [1]. Our approach can be straightforwardly extended to also incorporate relativistic corrections and, therefore, it will allow a complete and correct description of galaxy clustering at the largest scales.…”