Bispectrum-window convolution via Hankel transform

Abstract

We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the bispectrum, taking advantage of a 2D-FFTlog algorithm. As a preliminary test of its accuracy, we consider the toy model of a spherical window function in real space. This setup provides an analytical evaluation of the 3-point function of the window, and therefore it allows to isolate and quantify possible systematic errors of the method. We find that our implementation of the convolution in terms of a mixing matrix shows differences at the percent level in comparison to the measurements from a very large set of mock halo catalogs. It is also able to recover unbiased constraints on halo bias parameters in a likelihood analysis of a set of numerical simulations with a total volume of 100 h -3 Gpc3. For the level of accuracy required by these tests, the multiplication with the mixing matrix is performed in the time of one second or less.

New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies

“…For example, studies of the quadrupole bispectrum using 's method have mainly dealt only with the M = 0 mode (D' Amico et al 2022b). One reason is that the correction formula for the window function effect is only given for the M = 0 case (Pardede et al 2022). Moreover, we show in Section 7 that ζ112 gives additional cosmological information to ζ202, pointing out the importance of the M = 0 modes.…”

Window function convolution with deep neural network models

“…The bottleneck operation in the DNN approach is the creation of the training data set, which requires a significant time investment in the case of the bispectrum (in our case, the calculation of the 2000 convolved bispectra with 64 processor cores took approximately one month of wall-clock time). This step can be sped up using massive parallelisation and, possibly, by relying on more computationally friendly formulations of the convolution integral (e.g., Pardede et al 2022). It is also conceivable that using larger input vectors that densely sample the wavenumbers within shells of size ∆k around the output configurations might facilitate the task of the machine, and would thus help to reduce the training data.…”

“…Sugiyama et al (2019) introduced a new bispectrum estimator based on the tri-polar spherical harmonic decomposition with zero total angular momentum and showed, in this case, that it is possible to compute the models for the convolved bispectrum following a FFT-based approach. The issue of developing a similar method for more traditional estimators of the bispectrum multipoles (Scoccimarro 2015) has been recently addressed by Pardede et al (2022), who derived an expression based on two-dimensional Hankel transforms that can be computed using the 2D-FFTlog method (Fang et al 2020). In this case the survey window is described in terms of the multipoles of its three-point correlation function.…”

Cosmology with the Galaxy Bispectrum Multipoles: Optimal Estimation and Application to BOSS Data

“…Due to its oscillatory nature, this is a difficult and time-consuming numerical operation (though see Ref. [52] for a possible = 0 approach), thus the effect is often ignored or heavily simplified [e.g., 10,11,26,73,75,101,102]. This may lead to biases in data-analysis when large-scale modes (relevant to primordial non-Gaussianity studies) are included.…”

“…This allows us to avoid making simplified assumptions about the window function's action, which have led to the excision of large-scale modes in [26]; this could severely limit analyses of primordial non-Gaussianity. Whilst analytic methods for bispectrum convolution now exist (at least for the monopole, see [e.g., 52,53] for recent progress), this route still leads to a significant amplification in model complexity, which may make typical Monte Carlo Markov Chain (MCMC) analyses (with ∼ 10 6 steps [54]) infeasible. Our efforts herein are a natural extension of our previous full-shape BOSS analyses of the galaxy power spectrum [55][56][57], BAO [58], real-space power spectrum proxy [59], and bispectrum monopole [16,60,61], based on the effective field theory of large-scale structure (EFTofLSS; [62][63][64][65]).…”