Rees-Sciama Effect in a CDM Universe

The Rees-Sciama (RS) effect produces fluctuations in the cosmic microwave background (CMB) through the time-dependent gravitational potential in the nonlinear stages of evolution. I investigate the RS effect on the CMB angular power spectrum $C_l$ for several CDM models by combining the results of N-body simulations with second order perturbation theory. The amplitude of the RS fluctuations peaks at $l \sim 100-300$, where it gives $\Delta T /T \sim 10^{-7}-10^{-6}$ for a wide range of models. This is at least an order of magnitude below the COBE normalized primary contribution. RS fluctuations could be a dominant source of anisotropies only on subarcminute scales ($l \approx 5000$) and are below the present day observational sensitivities on all angular scales.