Covariance of the galaxy angular power spectrum with the halo model

Abstract

As the determination of density fluctuations becomes more precise with larger surveys, it becomes more important to account for the increased covariance due to the non-linearity of the field. Here I have focussed on the galaxy density, with analytical prediction of the non-Gaussianity using the halo model coupled with standard perturbation theory in real space. I carried out an exact and exhaustive derivation of all tree-level terms of the non-Gaussian covariance of the galaxy $C_{\ell }$, with the computation developed up to the third order in perturbation theory and local halo bias, including the non-local tidal tensor effect. A diagrammatic method was used to derive the involved galaxy 3D trispectra, including shot-noise contributions. The projection to the angular covariance was derived in all trispectra cases with and without Limber's approximation, with the formulae being of potential interest for other observables than galaxies. The effect of subtracting shot-noise from the measured spectrum is also discussed, and does simplify the covariance, though some non-Gaussian shot-noise terms still remain. I make the link between this complete derivation and partial terms which have been used previously in the literature, including super-sample covariance (SSC). I uncover a wealth of additional terms which were not previously considered, including a whole new class which I dub braiding terms as it contains multipole-mixing kernels. The importance of all these new terms is discussed with analytical arguments. I find that they become comparable to, if not bigger than, SSC if the survey is large or deep enough to probe scales comparable with the matter-radiation equality $k_{\mathrm{eq}}$. A short self-contained summary of the equations is provided in Section 9 for the busy reader, ready to be implemented numerically for analysis of current and future galaxy surveys.

18+17 pages, 3+4 figures. Updated to match version published in Astronomy & Astrophysics

References in corpus (8)

• Extended Limber Approximation
• Gravity and Large-Scale Non-local Bias
• Analysis of two-point statistics of cosmic shear: III. Covariances of shear measures made easy
• Complete super-sample lensing covariance in the response approach
• Massive data compression for parameter-dependent covariance matrices
• On the insufficiency of arbitrarily precise covariance matrices: non-Gaussian weak lensing likelihoods
• Quantifying lost information due to covariance matrix estimation in parameter inference
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• Self-calibration of weak lensing systematic effects using combined two- and three-point statistics
• Fast and easy super-sample covariance of large scale structure observables
• Disconnected Covariance of 2-point Functions in Large-Scale Structure
• Precise and Accurate Cosmology with CMBxLSS Power Spectra and Bispectra
• The Halo Void (Dust) Model of Large Scale Structure
• Debiasing inference with approximate covariance matrices and other unidentified biases
• Cosmological Angular Trispectra and Non-Gaussian Covariance
• COVMOS: a new Monte Carlo approach for galaxy clustering analysis
• Impact of survey geometry and super-sample covariance on future photometric galaxy surveys
• High resolution tomography for galaxy spectroscopic surveys with angular redshift fluctuations
• The impact of braiding covariance and in-survey covariance on next-generation galaxy surveys
• KiDS-Legacy: Covariance validation and the unified OneCovariance framework for projected large-scale structure observables
• Forecasting Super-Sample Covariance in Future Weak Lensing Surveys with SuperSCRAM
• Cosmology in the non-linear regime : the small scale miracle
• Efficient computation of the super-sample covariance for stage IV galaxy surveys
• Cosmological inference including massive neutrinos from the matter power spectrum: biases induced by uncertainties in the covariance matrix
• Fast and spurious: a robust determination of our peculiar velocity with future galaxy surveys