Signs of interacting vacuum and dark matter in the universe

We consider the impact of dynamical dark energy (DDE) in the possible solution of the existing tensions in the Lambda CDM. We test both interacting and non-interacting DE models with dark matter (DM). Among the former, the running vacuum model (RVM) interacting with DM appears as a favored option. The non-interacting scalar field model based on the potential V similar to phi(-alpha), and the generic XCDM parametrization, also provide consistent signs of DDE. The important novelty of our analysis with respect to the existing ones in the literature is that we use the matter bispectrum, together with the power spectrum. Using a complete and updated set of cosmological observations on SNIa+BAO+H(z)+LSS+CMB, we find that the crucial triad BAO+LSS+CMB (i.e. baryonic acoustic oscillations, large scale structure formation data and the cosmic microwave background) provide the bulk of the signal. The bispectrum data is instrumental to get hold of the DDE signal, as our analysis shows. If the bispectrum is not included, the DDE signal could not be currently perceived at a significant confidence level.