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tokens: by cutting the first 10 multipoles. Figure 6. We plot the SNR for the optimistic Euclid cluster survey (Eu_cl_opt) as a function of l min (top left), the maximum redshift probed by the survey (top right), the area of the sky survey (bottom left), and the minimum observed mass as over the redshift range 0.2 ≤ ≤ 2 (bottom right). Dashed line represents the expected SNR for the Eu_cl_opt specifications. All the SNR take into account of the contribution from CMB E-mode polarization according to equation ( 21 ). Bottom left-hand panel of Fig. 6 shows the SNR as a function of the observed sky fraction, which does not affect just equation ( 21 ) as SNR, but it changes also the amount of total clusters observed, i.e. the shot-noise error. The SNR is sufficiently robust to a reduction of max ; the forecast SNR remains above a detection for max ≳ 1.4 for the optimistic Euclid cluster survey when the CMB polarization is added. We finally study the dependence of the SNR when changing M min . We vertically shift a redshift independent selection function around 8 × 10 13 M ⊙ , as representative of the selection function from (Sartoris et al. 2016 ) for the photometric Euclid cluster survey. The results in Fig. 6 (bottom left-hand panel) show that the expected selection function for Euclid would be optimal in terms of SNR. We can conclude that for the ISW detection is more important to have wide surveys, covering a large fraction of the sky, than deeper ones, since the surveys analysed are already signal dominated on the scales relevant for the ISW. We now briefly discuss the dependence of the SNR on the underlying cosmology. The cross-correlation power spectrum is sensitive to the total matter density Ω m and to the dark energy equation of state 0 . They both change the amplitude of (since for a flat universe an increased amount of matter density corresponds to have a smaller amount of dark energy density). Moreover, the peak of is shifted according to a different matter-dark energy equivalence. We show the dependence of the SNR on these two parameters in Fig. 7 by keeping fixed all the other cosmological parameters (note that we change σ 8 according to the variation of Ω m and 0 ). The SNR varies less than when we change Ω m up to away from the Planck best fit (Aghanim et al. 2016 ). We find a stronger effect on the dark energy parameter of state 0 . Even a small shift of Δ 0 ≃ 0.2 would lead to a difference larger than on the SNR. In particular, by assuming a fiducial cosmology with a smaller value of 0 leads to a higher SNR. Figure 7. Top panel: dependence on Ω m of the SNR for the ISW detection with clusters (optimistic Euclid cluster survey, blue line) and with galaxies (photometric Euclid galaxy survey, grey line). Bottom panel: dependence on the dark energy equation of state 0 of the SNR for the ISW detection. 5.2 Combining clusters with galaxies Different LSS surveys can be combined to increase the significance of the ISW detection. The