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.
