Degeneracy between nonadiabatic dark energy models and $\Lambda$CDM: ISW effect and the cross correlation of CMB with galaxy clustering data

As recently pointed out in Ref. [Phys.\ Rev.\ D {\bf 96}, 8, 083502 (2017)] the evolution of the linear matter perturbations in nonadiabatic dynamical dark energy models is almost indistinguishable (quasi-degenerated) to the standard $\Lambda$CDM scenario. In this work we extend this analysis to CMB observables in particular the integrated Sachs-Wolfe effect and its cross-correlation with large scale structure. We find that this feature persists for such CMB related observable reinforcing that new probes and analysis are necessary to reveal the nonadiabatic features in the dark energy sector.