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Making cosmological inferences from the observed galaxy clustering requiresaccurate predictions for the mean clustering statistics and their covariances.Those are affected by cosmic variance -- the statistical noise due to thefinite number of harmonics. The cosmic variance can be suppressed by fixing theamplitudes of the harmonics instead of drawing them from a Gaussiandistribution predicted by the inflation models. Initial realizations also canbe generated in pairs with 180 degrees flipped phases to further reduce thevariance. Here, we compare the consequences of using paired-and-fixed vsGaussian initial conditions on the average dark matter clustering andcovariance matrices predicted from N-body simulations. As in previous studies,we find no measurable differences between paired-and-fixed and Gaussiansimulations for the average density distribution function, power spectrum andbispectrum. Yet, the covariances from paired-and-fixed simulations aresuppressed in a complicated scale- and redshift-dependent way. The situation isparticularly problematic on the scales of Baryon Acoustic Oscillations wherethe covariance matrix of the power spectrum is lower by only 20% compared tothe Gaussian realizations, implying that there is not much of a reduction ofthe cosmic variance. The non-trivial suppression, combined with the fact thatpaired-and-fixed covariances are noisier than from Gaussian simulations,suggests that there is no path towards obtaining accurate covariance matricesfrom paired-and-fixed simulations. Because the covariances are crucial for theobservational estimates of galaxy clustering statistics and cosmologicalparameters, paired-and-fixed simulations, though useful for some applications,cannot be used for the production of mock galaxy catalogs.

Suppressing cosmic variance with paired-and-fixed cosmological simulations: average properties and covariances of dark matter clustering statistics