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The present density of Dark Energy almost equals the density of Dark Matter, although the two components have very different properties. In most models the Dark Matter density decreased almost a billion times more than the Dark Energy density from recombination to now - and yet the two quantities are almost identical today. This coincidence constitutes the "why now" problem of Dark Energy. It is common to the cosmological constant and even to most standard quintessence scenarios, which predict that Dark Matter diluted with expansion much faster than Dark Energy. The coincidence problem motivated the idea that Dark Energy and Dark Matter actually "know" each other through a direct interaction. In these models the two components settle down eventually into a state in which they behave as a single fluid at the background level. In a class of such models Dark Energy couples to a Dark Matter component or to massive neutrinos, inducing a growth of the particles' mass.

"Growing neutrino quintessence", in particular, predicts a precise relation between the neutrino mass and their abundance on one side, and the present Dark Energy density and the equation of state on the other side. The onset of the cosmic acceleration is triggered by neutrinos becoming non-relativistic, providing for a possible solution of the "why now" problem. The model predicts observable phenomena, in particular a fast growth of neutrino perturbations and the possible formation of large neutrino clumps. In these models the Dark Energy equation of state is similar to Dark Matter as long as neutrinos remain non-relativistic, as in Early Dark Energy scenarios.

This project extends the analysis of these models, both at the linear and the non-linear level (in particular concerning the Cosmic Microwave Background, the matter power spectrum, and the formation of neutrino clumps). New forecasts for future large-scale surveys are produced and new observables that can help reconstruct the cosmic expansion (like the redshift drift and the cosmic parallax) are investigated.

The models with interacting dark components can be reviewed as a simple but phenomenologically rich class of modified gravity theories. It is important to forecast how well future surveys will constrain the new parameters and which mix of cosmological probes is best suited to test the model properties. This is strongly connected to project **B11** (*Analysis and Forecast for Large-Scale Dark Energy Surveys*).

Further, there is a close link to project **C3** (*Dark Matter-Dark Energy interactions*).
The numerical simulations of interacting models by N-body codes will provide additional important constraints on the model and guidance on the interesting parameter ranges. Conversely, the selection of the models to investigate through numerical simulations will need a preliminary study of the background and linear properties.

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