CARPool Covariance: Fast, unbiased covariance estimation for large-scale structure observables

The covariance matrix $\boldsymbol{\Sigma}$ of non-linear clustering statistics that are measured in current and upcoming surveys is fundamental interest for comparing cosmological theory data a crucial ingredient the likelihood approximations underlying widely used parameter inference forecasting methods. extreme number simulations needed to estimate sufficient accuracy poses severe challenge. Approximating using inexpensive but biased surrogates introduces model error with respect full simulations, especially regime structure growth. To address this problem we develop generalization Convergence Acceleration by Regression Pooling (CARPool) combine small fast obtain low-noise estimates unbiased construction. Our numerical examples use CARPool GADGET-III $N$-body computed COmoving Lagrangian (COLA). Even at challenging redshift $z=0.5$, find variance reductions least $\mathcal{O}(10^1)$ up $\mathcal{O}(10^4)$ elements matter power spectrum on scales $8.9\times 10^{-3}<k_\mathrm{max} <1.0$ $h {\rm Mpc^{-1}}$. We demonstrate comparable performance bispectrum, correlation function probability density field. compare eigenvalues, likelihoods, Fisher matrices standard sample estimators generally considerable improvement except cases where $\Sigma$ severely ill-conditioned.