Estimating small angular scale CMB anisotropy with high resolution N-body simulations: weak lensing

We estimate the impact of weak lensing by strongly nonlinear cosmological structures on the cosmic microwave background. Accurate calculation of large $\ell$ multipoles requires N-body simulations and ray-tracing schemes with both high spatial and temporal resolution. To this end we have developed a new code that combines a gravitational Adaptive Particle-Particle, Particle-Mesh (AP3M) solver with a weak lensing evaluation routine. The lensing deviations are evaluated while structure evolves during the simulation so that all evolution steps--rather than just a few outputs--are used in the lensing computations. The new code also includes a ray-tracing procedure that avoids periodicity effects in a universe that is modeled as a 3-D torus in the standard way. Results from our new simulations are compared with previous ones based on Particle-Mesh simulations. We also systematically investigate the impact of box volume, resolution, and ray-tracing directions on the variance of the computed power spectra. We find that a box size of $512 h^{-1}$ Mpc is sufficient to provide a robust estimate of the weak lensing angular power spectrum in the $\ell$-interval (2,000--7,000). For a reaslistic cosmological model the power $[\ell(\ell+1)C_{\ell}/2\pi]^{1/2}$ takes on values of a few $\mu K$ in this interval, which suggests that a future detection is feasible and may explain the excess power at high $\ell$ in the BIMA and CBI observations.