The impact of braiding covariance and in-survey covariance on next-generation galaxy surveys

TL;DR

This paper investigates the effects of non-Gaussian covariance, including braiding covariance, on galaxy survey parameter constraints, showing that accounting for these effects significantly increases error estimates and improves robustness of cosmological inferences.

Contribution

It introduces an efficient approximation for braiding covariance and demonstrates its necessity for accurate non-Gaussian covariance modeling in galaxy surveys.

Findings

Including braiding covariance increases parameter error bars by up to 120%.

Non-Gaussian terms reduce parameter degeneracies, enhancing constraint robustness.

Accounting for all non-Gaussian covariance components is essential for accurate forecasts.

Abstract

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]