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 $\mathrm{\Lambda }$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 $C_{ij}(\mathrm{\ell })$ for 5 or 10 tomographic bands. We find that shear spectra obtained by using 128 $h^{-1}$Mpc simulations can vary up to $\sim 25\mathrm{\%}$, just because of the seed. Sample variance lowers to $\sim 3.3\mathrm{\%}$, 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 $\sim 1\mathrm{\%}$ precision expected for data, if still using 8 boxes, we require a size $\sim 1300$--$ 1700 , h^{-1}$ Mpc for them.