Sample variance in N--body simulations and impact on tomographic shear predictions

We study the effects of sample variance in N--body simulations, as a function of the size of the simulation box, namely in connection with predictions on tomographic shear spectra. We make use of a set of 8 $Λ$CDM simulations in boxes of 128, 256, 512 $h^{-1}$Mpc aside, for a total of 24, differing just by the initial seeds. Among the simulations with 128 and 512 $h^{-1}$Mpc aside, we suitably select those closest and farthest from {\it average}. Numerical and linear spectra $P(k,z)$ are suitably connected at low $k$ so to evaluate the effects of sample variance on shear spectra $C_{ij}(\ell)$ for 5 or 10 tomographic bands. We find that shear spectra obtained by using 128 $h^{-1}$Mpc simulations can vary up to $\sim 25\, \%$, just because of the seed. Sample variance lowers to $\sim 3.3\, \%$, when using 512 $h^{-1}$Mpc. These very percentages could however slightly vary, if other sets of the same number of realizations were considered. Accordingly, in order to match the $\sim 1\, \%$ precision expected for data, if still using 8 boxes, we require a size $\sim 1300$ --$1700 \, h^{-1}$ Mpc for them.

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