Research Note

Absence of significant cross-correlation between WMAP and SDSS

¹ Instituto de Astrofísica de Canarias, 38200 La Laguna, Tenerife, Spain e-mail: martinlc@iac.es
² Departamento de Astrofísica, Universidad de La Laguna, 38205 La Laguna, Tenerife, Spain
³ Centro Studi e Ricerche Enrico Fermi, via Panisperna 89 A, Compendio del Viminale, 00184 Rome, Italy
⁴ Istituto dei Sistemi Complessi CNR, via dei Taurini 19, 00185 Rome, Italy

Received: 25 June 2009
Accepted: 17 January 2010

Abstract

Aims. Several authors have claimed to detect a significant cross-correlation between microwave WMAP anisotropies and the SDSS galaxy distribution. We repeat these analyses to determine the different cross-correlation uncertainties caused by re-sampling errors and field-to-field fluctuations. The first type of error concerns overlapping sky regions, while the second type concerns non-overlapping sky regions.

Methods. To measure the re-sampling errors, we use bootstrap and jack-knife techniques. For the field-to-field fluctuations, we use three methods: 1) evaluation of the dispersion in the cross-correlation when correlating separated regions of WMAP with the original region of SDSS; 2) use of mock Monte Carlo WMAP maps; 3) a new method (developed in this article), which measures the error as a function of the integral of the product of the self-correlations for each map.

Results. The average cross-correlation for b > 30 deg is significantly stronger than the re-sampling errors – both the jack-knife and bootstrap techniques provide similar results – but it is of the order of the field-to-field fluctuations. This is confirmed by the cross-correlation between anisotropies and galaxies in more than the half of the sample being null within re-sampling errors.

Conclusions. Re-sampling methods underestimate the errors. Field-to-field fluctuations dominate the detected signals. The ratio of signal to re-sampling errors is larger than unity in a way that strongly depends on the selected sky region. We therefore conclude that there is no evidence yet of a significant detection of the integrated Sachs-Wolfe (ISW) effect. Hence, the value of Ω ≈ 0.8 obtained by the authors who assumed they were observing the ISW effect would appear to have originated from noise analysis.