Cross-correlation between the cosmic microwave and infrared backgrounds for integrated Sachs–Wolfe detection

We investigate the cross-correlation between the cosmic infrared background (CIB) and cosmic microwave background (CMB) anisotropies due to the integrated Sachs–Wolfe (ISW) effect. We first describe the CIB anisotropies using a linearly biased power spectrum, valid on the angular scales of interest. From this, we derive the theoretical angular power spectrum of the CMB–CIB cross-correlation for different instruments and frequencies. Our cross-spectra show similarities in shape with usual CMB–galaxies cross-correlations. We discuss the detectability of the ISW signal by performing a signal-to-noise ratio (S/N) analysis with our predicted spectra. Our results show that (i) in the ideal case of noiseless, full-sky maps, the significances obtained range from 6σ to 7σ depending on the frequency, with a maximum at 353 GHz, and (ii) in realistic cases which account for the presence of noise including astrophysical contaminants, the results depend strongly on the major contribution to the noise term. They span from 2σ to 5σ, the most favourable frequency for detection being 545 GHz. We also find that the joint use of all available frequencies in the cross-correlation does not improve significantly the total S/N, due to the high level of correlation of the CIB maps at different frequencies.