Integrated Sachs-Wolfe effect in cross-correlation: The observer's manual

The Integrated Sachs-Wolfe (ISW) effect is a direct signature of the presence of dark energy in the universe, in the absence of spatial curvature. A powerful method for observing the ISW effect is through cross-correlation of the cosmic microwave background with a tracer of the matter in the low redshift universe. In this paper, we describe the dependence of the obtained cross-correlation signal on the geometry and other properties of a survey of the low redshift universe. We show that an all-sky survey with about $10\times {10}^6$ galaxies, almost uniformly distributed within $0<z<1$ should yield a near optimal ISW detection, at $\sim 5\sigma$ level. In order to achieve this level of signal-to-noise, the systematic anisotropies in the survey must be below $\sim 0.1\%$, on the scale of $\sim 10°$ on the sky, while the systematic error in redshift estimates must be less than 0.05. Then, we argue that, while an ISW detection will not be a good way of constraining the conventional properties of dark energy, it could be a valuable means of testing alternative theories of gravity on large physical scales.