Impact of scale dependent bias and nonlinear structure growth on the integrated Sachs-Wolfe effect: Angular power spectra

Abstract

We investigate the impact of nonlinear evolution of the gravitational potentials in the ΛCDM model on the integrated Sachs-Wolfe (ISW) contribution to the cosmic microwave background (CMB) temperature power spectrum, and on the cross-power spectrum of the CMB and a set of biased tracers of the mass. We use an ensemble of N-body simulations to directly follow the potentials and compare the results to analytic PT methods. The predictions from the PT match the results to high precision for k<0.2hMpc-1. We compute the nonlinear corrections to the angular power spectrum and find them to be <10% of linear theory for l<100. These corrections are swamped by the cosmic variance. On scales l>100 the departures are more significant; however, the CMB signal is more than a factor 103 larger at this scale. Nonlinear ISW effects therefore play no role in shaping the CMB power spectrum for l<1500. We analyze the CMB-density tracer cross spectrum using simulations and renormalized bias PT, and find good agreement. The usual assumption is that nonlinear evolution enhances the growth of structure and counteracts the linear ISW on small scales, leading to a change in sign of the CMB large-scale structure cross spectrum at small scales. However, PT analysis suggests that this trend reverses at late times when the logarithmic growth rate f=dlnD/dlna<0.5 or Ωm(z)<0.3. Numerical results confirm these expectations and we find no sign change in ISW large-scale structure cross power for low redshifts. Corrections due to nonlinearity and scale dependence of the bias are found to be <10% for l<100, and are therefore below the signal to noise of the current and future measurements. Finally, we estimate the cross-correlation coefficient between the CMB and halos and show that it can be made to match that for the dark matter and CMB to within 5% for thin redshift shells, thus mitigating the need to model bias evolution. © 2009 The American Physical Society.