Impact of scale-dependent bias and nonlinear evolution on the ISW
  I summarize recent results from Smith, Hernandez-Monteagudo & Seljak (2009),
a study of the impact of nonlinear evolution of gravitational potentials in the
LCDM model on the Integrated Sachs-Wolfe (ISW) contribution to the cross-power
spectrum of the CMB and a set of biased tracers of the mass. We use a large
ensemble of N-body simulations to directly follow the potentials and compare
the results to analytic perturbation theory (PT) methods. The PT predictions
match our results to high precision for k<0.2 Mpc/h. 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-LSS cross-spectrum at small scales. However, PT
analysis suggests that this trend reverses at late times when the logarithmic
growth rate f=d ln D/d ln a<1/2 or Omega_m (z)<0.3. Numerical results confirm
these expectations and we find nonlinear enhancement of the ISW signal on small
scales at late-times. On computing the total contribution to the angular
spectrum, we find that nonlinearity and scale dependence of the bias are unable
to influence the signal-to-noise of the current and future measurements.
