The concordance particle creation model -a class of Λ(t)CDM cosmologies -is studied using large scale structure (LSS) formation, with particular attention to the integrated Sachs-Wolfe (ISW) effect. The evolution of the gravitational potential and the amplitude of the cross-correlation of the cosmic microwave background (CMB) signal with LSS surveys are calculated in detail. We properly include in our analysis the peculiarities involving the baryonic dynamics of the Λ(t)CDM model which were not included in previous works. Although both the Λ(t)CDM and the standard cosmology are in agreement with available data for the CMB-LSS correlation, the former presents a slightly higher signal which can be identified with future data.

We study structure formation using relativistic cosmological linear perturbation theory in the presence of intrinsic and relative (with respect to matter) non-adiabatic dark energy perturbations. For different dark energy models we assess the impact of non-adiabaticity on the matter growth promoting a comparison with growth rate data. The dark energy models studied lead to peculiar signatures of the (non)adiabatic nature of dark energy perturbations in the evolution of the f σ8(z) observable. We show that non-adiabatic DE models become close to be degenerated with respect to the ΛCDM model at first order in linear perturbations. This would avoid the identification of the non-adiabatic nature of dark energy using current available data. Therefore, such evidence indicates that new probes are necessary to reveal the non-adiabatic features in the dark energy sector.PACS numbers: 04.50. Kd, 95.36.+x,

We calculate the skewness (the third moment S3) of matter distribution in dynamical dark energy cosmologies. We pay particular attention to the impact of dark energy perturbations on this quantity. There is indeed a clear signature of dark energy perturbations on this quantity. By properly allowing dark energy perturbations we show that their impact on S3 is strong enough (a factor ∼ 3 greater) to easily discriminate between clustering and non-clustering dark energy cosmologies. This indicates that high order statistics of the cosmic density field are useful to the study of dark energy models and are potentially able to rule out clustering dark energy cosmologies.

As recently pointed out in Ref. [Phys. Rev. D 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 ΛCDM 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.

We investigate the role played by dark energy perturbations in the skewness S3 of large-scale matter distribution. We consider a two-fluid universe composed by matter and dark energy, with perturbations in both components, and we estimate numerically the skewness of the matter density field as a function of the dark energy parameters. We characterize today's S3 value for quintessence and phantom dark energy cosmologies as well as its dependence on the matter density parameter Ωm0 and the dark energy sound speed c 2 s with accurate numerical fitting. These fits can be used to test cosmology against future high quality data on large scale structure.