Covariance of the galaxy angular power spectrum with the halo model

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

Super-sample covariance approximations and partial sky coverage

Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.Comment: 14 pages, 10 figures. Updated to match version published in Astronomy & Astrophysic

Non-Gaussianity of the Cosmic Infrared Background anisotropies II : Predictions of the bispectrum and constraints forecast

Using a full analytical computation of the bispectrum based on the halo model together with the halo occupation number, we derive the bispectrum of the cos- mic infrared background (CIB) anisotropies that trace the clustering of dusty-star- forming galaxies. We focus our analysis on wavelengths in the far-infrared and the sub-millimeter typical of the Planck/HFI and Herschel/SPIRE instruments, 350, 550, 850, and 1380 um. We explore the bispectrum behaviour as a function of several models of evolution of galaxies and show that it is strongly sensitive to that ingredient. Contrary to the power spectrum, the bispectrum, at the four wavelengths, seems dominated by low redshift galaxies. Such a contribution can be hardly limited by applying low flux cuts. We also discuss the contributions of halo mass as a function of the redshift and the wavelength, recovering that each term is sensitive to a different mass range. Furthermore, we show that the CIB bispectrum is a strong contaminant of the Cosmic Microwave Background bispectrum at 850 um and higher. Finally, a Fisher analysis of the power spectrum, bispectrum alone and of the combination of both shows that degeneracies on the HOD parameters are broken by including the bispectrum information, leading to tight constraints even when including foreground residuals.Comment: 16 pages, Accepted by MNRA

Cosmology in the non-linear regime : the small scale miracle

Interest rises to exploit the full shape information of the galaxy power spectrum, as well as pushing analyses to smaller non-linear scales. Here I use the halo model to quantify the information content in the tomographic angular power spectrum of galaxies, for future high resolution surveys : Euclid and SKA2. I study how this information varies as a function of the scale cut applied, either with angular cut $\ell_{max}$ or physical cut kmax. For this, I use analytical covariances with the most complete census of non-Gaussian terms, which proves critical. I find that the Fisher information on most cosmological and astrophysical parameters follows a striking behaviour. Beyond the perturbative regime we first get decreasing returns : the information keeps rising but the slope slows down until reaching a saturation. The location of this plateau is a bit beyond the reach of current modeling methods : k $\sim$ 2 Mpc$^{-1}$ and slightly depends on the parameter and redshift bin considered. I explain the origin of this plateau, which is due to non-linear effects both on the power spectrum, and more importantly on non-Gaussian covariance terms. Then, pushing further we see the information rising again in the highly non-linear regime, with a steep slope. This is the small scale miracle, for which I give interpretation and discuss the properties. Hints are shown that this information should be disentanglable from the astrophysical content, and could improve Dark Energy constraints. Finally, more hints are shown that high order statistics may yield significant improvements over the power spectrum in this regime, with the improvements increasing with kmax. Data and notebooks reproducing all plots and results will be made available at \url{https://github.com/fabienlacasa/SmallScaleMiracle}Comment: 9+3 pages, 10+5 figures. Updated to answer referees comments, new model in appendi

Non-Gaussianity of the Cosmic Infrared Background anisotropies I : Diagrammatic formalism and application to the angular bispectrum

We present the first halo model based description of the Cosmic Infrared Background (CIB) non-Gaussianity (NG) that is fully parametric. To this end, we introduce, for the first time, a diagrammatic method to compute high order polyspectra of the 3D galaxy density field. It allows an easy derivation and visualisation of the different terms of the polyspectrum. We apply this framework to the power spectrum and bispectrum, and we show how to project them on the celestial sphere in the purpose of the application to the CIB angular anisotropies. Furthermore, we show how to take into account the particular case of the shot noise terms in that framework. Eventually, we compute the CIB angular bispectrum at 857 GHz and study its scale and configuration dependencies, as well as its variations with the halo occupation distribution parameters. Compared to a previously proposed empirical prescription, such physically motivated model is required to describe fully the CIB anisotropies bispectrum. Finally, we compare the CIB bispectrum with the bispectra of other signals potentially present at microwave frequencies, which hints that detection of CIB NG should be possible above 220 GHz.Comment: 21 pages, 21 figures. Accepted by MNRA

Statistical effects of the observer's peculiar velocity on source number counts

The velocity of the Sun with respect to the cosmic microwave background (CMB) can be extracted from the CMB dipole, provided its intrinsic dipole is assumed to be small in comparison. This interpretation is consistent, within fairly large error bars, with the measurement of the correlations between neighboring CMB multipoles induced by the velocity of the observer, which effectively breaks isotropy. In contrast, the source number count dipole was reported to privilege a velocity of the observer with an amplitude which is about twice as large as the one extracted from the entirely kinematic interpretation of the CMB dipole, with error bars which indicate a more and more significant tension. In this work, we study the effect of the peculiar velocity of the observer on correlations of nearby multipoles in the source number counts. We provide an unbiased estimator for the kinetic dipole amplitude, which is proportional to the peculiar velocity of the observer and we compute the expected signal to noise ratio. Near future experiments can achieve better than 5$\%$ constraints on the velocity of the Sun with our estimator.Comment: 12 pages, 1 figure, matches published versio