In this work we present a method to extract the signal induced by the
integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB).
It makes use of the Linear Covariance-Based filter introduced by Barreiro et
al., and combines CMB data with any number of large-scale structure (LSS)
surveys and lensing information. It also exploits CMB polarization to reduce
cosmic variance. The performance of the method has been thoroughly tested with
simulations taking into account the impact of non-ideal conditions such as
incomplete sky coverage or the presence of noise. In particular, three galaxy
surveys are simulated, whose redshift distributions peak at low (z≃0.3), intermediate (z≃0.6) and high redshift (z≃0.9). The
contribution of each of the considered data sets as well as the effect of a
mask and noise in the reconstructed ISW map is studied in detail. When
combining all the considered data sets (CMB temperature and polarization, the
three galaxy surveys and the lensing map), the proposed filter successfully
reconstructs a map of the weak ISW signal, finding a perfect correlation with
the input signal for the ideal case and around 80 per cent, on average, in the
presence of noise and incomplete sky coverage. We find that including CMB
polarization improves the correlation between input and reconstruction although
only at a small level. Nonetheless, given the weakness of the ISW signal, even
modest improvements can be of importance. In particular, in realistic
situations, in which less information is available from the LSS tracers, the
effect of including polarisation is larger. For instance, for the case in which
the ISW signal is recovered from CMB plus only one survey, and taking into
account the presence of noise and incomplete sky coverage, the improvement in
the correlation coefficient can be as large as 10 per cent.Comment: 17 pages, 15 figures, accepted for publication in MNRA
