http://arxiv.org/abs/1711.07372
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 focus on the galaxy density, with analytical prediction of the non-Gaussianity using the halo model coupled with standard perturbation theory. I carry 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 third order in perturbation theory and local halo bias, including the non-local tidal tensor effect. A diagrammatic method is used to derive the involved galaxy 3D trispectra, including shot-noise contributions. The projection to the angular covariance is 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 substracting 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, include 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 can 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.
F. Lacasa
Tue, 21 Nov 17
4/79
Comments: 18+17 pages, 3+4 figures