The impact of braiding covariance and in-survey covariance on
  next-generation galaxy surveys
  As galaxy surveys become more precise and push to smaller scales, the need
for accurate covariances beyond the classical Gaussian formula becomes more
acute. Here, I investigate the analytical implementation and impact of
non-Gaussian covariance terms that I previously derived for galaxy clustering.
Braiding covariance is such a class of terms and it gets contribution both from
in-survey and super-survey modes. I present an approximation for braiding
covariance which speeds up the numerical computation. I show that including
braiding covariance is a necessary condition for including other non-Gaussian
terms: the in-survey 2-, 3- and 4-halo covariance, which yield covariance
matrices with negative eigenvalues if considered on their own. I then quantify
the impact on parameter constraints, with forecasts for a Euclid-like survey.
Compared to the Gaussian case, braiding and in-survey covariances significantly
increase the error bars on cosmological parameters, in particular by 50% for w.
The Halo Occupation Distribution (HOD) error bars are also affected between 12%
and 39%. Accounting for super-sample covariance (SSC) also increases parameter
errors, by 90% for w and between 7% and 64% for HOD. In total, non-Gaussianity
increases the error bar on w by 120% (between 15% and 80% for other
cosmological parameters), and the error bars on HOD parameters between 17% and
85%. Accounting for the 1-halo trispectrum term on top of SSC is not sufficient
for capturing the full non-Gaussian impact: braiding and the rest of in-survey
covariance have to be accounted for. Finally, I discuss why the inclusion of
non-Gaussianity generally eases up parameter degeneracies, making cosmological
constraints more robust to astrophysical uncertainties. The data and a Python
notebook reproducing the results and plots of the article are available at
\url{https://github.com/fabienlacasa/BraidingArticle}. [Abridged]
