Abstract
In this paper we present for the first time the angular power spectra
$C_\ell(z,z')$ for number counts from relativistic N-body simulations. We use
the relativistic N-body code gevolution with its exact integration of lightlike
geodesics which include all relativistic scalar contributions to the number
counts. We compare our non-perturbative numerical results with the results from
CLASS using the Halofit approximation for the non-linear matter power spectrum.
We find that the Halofit approximation is excellent for both, the density field
and the convergence, but it cannot accurately model redshift-space distortions.
We also find that the largest contribution to the unequal-redshift power
spectra is the cross-correlation of the density and the lensing contribution to
the number count, especially for redshift bins that are far apart. Correlating
the number counts with the convergence map we find that the signal is dominated
by the lensing-lensing term when the convergence field redshift is not higher
than the number count one, while it is dominated by the density-lensing term in
the opposite case. In the present study, the issue of galaxy bias is
deliberately left aside by considering only unbiased samples of matter
particles from the simulations.
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