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

Abstract

As galaxy surveys become more precise with lower noise and pushing to small non-linear scales, the need for accurate covariances beyond the vanilla Gaussian formula becomes more acute. Here, I investigate the analytical implementation and impact of non-Gaussian covariance terms that I uncovered for the galaxy angular power spectrum (Lacasa 2018). Braiding covariance is such an interesting class of these new terms, that gets contribution both from in-survey and super-survey modes, the latter being hard to calibrate with simulations. I present an approximation to Braiding covariance making it fast to compute numerically. I show that accounting for Braiding covariance is necessary to include other non-Gaussian terms, namely the in-survey 2-, 3-and 4-halo covariance. Indeed the latter quantify coupling between large and small scales, and would yield incorrect covariance matrices with negative eigenvalues, if left alone. I then move to quantify the impact on parameter constraints, with forecasts for a survey with Euclid-like galaxy density and angular scales. Compared with the Gaussian case, Braiding and in-survey covariances significantly increase the error bars on all cosmological parameters of the wCDM model, in particular by 50% for the Dark Energy equation of state w. The error bars on Halo Occupation Distribution (HOD) parameters 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, as one in some current analyses, is not sufficient to capture the full non-Gaussian impact: Braiding and the rest of in-survey covariance have to be accounted for. I finally discuss why the inclusion of non-Gaussianity generally eases up parameter degeneracies, making cosmological constraints more robust to astrophysical uncertainties. Data and a notebook reproducing all plots and results are available at https://github. com/fabienlacasa/BraidingArticle Key words. methods: analytical -large-scale structure of the universe Article number, page 1 of 10

Impact of survey geometry and super-sample covariance on future photometric galaxy surveys

“…Many works have shown that the SSC can have a large impact on cosmological constraints coming from a variety of standard cosmological probes (Hu & Kravtsov 2003;Barreira et al 2018a;Lacasa 2020). Most studies focused on describing the SSC using the approximation of flat-sky or full-sky (Lacasa & Rosenfeld 2016;Lacasa & Grain 2019).…”

“…First discovered for cluster counts (Hu & Kravtsov 2003), a vast amount of literature has been devoted to the SSC in recent years (e.g. Takada & Hu 2013;Takada & Spergel 2014;Takahashi et al 2014;Li et al 2018;Chan et al 2018;Lacasa & Kunz 2017;Lacasa et al 2018;Barreira et al 2018a,b), and it is well known to have a large impact on constraints on the dark energy equation of state for future surveys, be it for clusters (Hu & Kravtsov 2003), weak lensing (Barreira et al 2018a), or photometric galaxy clustering Lacasa (2020).…”

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

“…Targeting non-linear scales also introduces more complex statistical problems: the matter-galaxy density field becomes significantly non-Gaussian, which increases the error bars due to non-Gaussian covariance terms. In the present article, I build upon the work of Lacasa (2018Lacasa ( , 2020 who developed a near complete modelling of these non-Gaussian terms using the halo model and the HOD.…”

“…We see that the 3h-base and 4h-3 terms are negligible for this variance. Indeed, Lacasa (2020) found that they have a negligible impact on the total covariance and on the parameter constraints up to max = 2000. Here, I find this result to still hold to max = 20 000.…”

“…However, the Gaussian formula does not capture the full covariance, especially on small scales. In this article, I follow the equations for the non-Gaussian part of the covariance from Lacasa (2018), and the numerical approximation and implementation of Lacasa (2020). For the article to be self-contained, I summarise the involved terms.…”