Measuring the integrated Sachs-Wolfe effect

Context. One of the main challenges of modern cosmology is to understand the nature of the mysterious dark energy that causes the cosmic acceleration. The integrated Sachs-Wolfe (ISW) effect is sensitive to dark energy, and if detected in a universe where modified gravity and curvature are excluded, presents an independent signature of dark energy. The ISW effect occurs on large scales where cosmic variance is high and where owing to the Galactic confusion we lack large amounts of data in the CMB as well as large-scale structure maps. Moreover, existing methods in the literature often make strong assumptions about the statistics of the underlying fields or estimators. Together these effects can severely limit signal extraction. Aims. We aim to define an optimal statistical method for detecting the ISW effect that can handle large areas of missing data and minimise the number of underlying assumptions made about the data and estimators. Methods. We first review current detections (and non-detections) of the ISW effect, comparing statistical subtleties between existing methods, and identifying several limitations. We propose a novel method to detect and measure the ISW signal. This method assumes only that the primordial CMB field is Gaussian. It is based on a sparse inpainting method to reconstruct missing data and uses a boot-strap technique to avoid assumptions about the statistics of the estimator. It is a complete method, which uses three complementary statistical methods. Results. We apply our method to Euclid-like simulations and show we can expect a similar to 7 sigma model-independent detection of the ISW signal with WMAP7-like data, even when considering missing data. Other tests return similar to 5 sigma detection levels for a Euclid-like survey. We find that detection levels are independent from whether the galaxy field is normally or lognormally distributed. We apply our method to the 2 Micron All Sky Survey (2MASS) and WMAP7 CMB data and find detections in the 1.0-1.2 sigma range, as expected from our simulations. As a by-product, we have also reconstructed the full-sky temperature ISW field from the 2MASS data. Conclusions. We present a novel technique based on sparse inpainting and bootstrapping, which accurately detects and reconstructs the ISW effect.