We explore the use of the cosmic infrared background as a tracer of the LSS for cross-correlating with the CMB and exploit the ISW. We use the improved linear CIB model of Maniyar et al (2018) and derive the theoretical CIBxISW cross-correlation for Planck HFI frequencies 217, 353, 545 and 857 GHz and IRAS 3000 GHz. We predict a positive cross-correlation between the CIB and CMB whose amplitude decreases rapidly at small scales. We perform a signal-to-noise ratio (SNR) analysis on this cross-correlation. In the ideal case of the cross-correlation obtained over 70% (40%) of the sky with no residual contaminants (e.g. galactic dust) in maps, the SNR ranges from 4.2-5.6 (3.2-4.3) with the highest for 857 GHz. A Fisher matrix analysis shows that an ISW signal detected with such high SNR on the 40% sky can improve the constraints on the cosmological parameters considerably; constraints on the equation of state of the dark energy are improved by 80%. We then perform a more realistic analysis with the effect of residual galactic dust contamination in CIB maps. We calculate the dust power spectra for several frequencies and sky fractions which dominate over CIB at lower multipoles we are interested in. Considering conservative 10% residual level of galactic dust in the CIB power spectra, we find that the SNR drops drastically making ISW detection difficult. To check the capability of current maps to detect ISW via this method, we measure the cross-correlation of the CIB and the CMB Planck maps on so called GASS field covering an area of 11% in the southern hemisphere. We find that with such a small sky fraction and dust residuals present in CIB maps, we do not detect ISW signal and the measured signal is consistent with zero. In order not to degrade the SNR for the ISW measurement by more than 10% on the 40% sky, we find that the dust needs to be cleaned up to 0.01% level on the power spectrum.
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