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We present a new approach to build models of quintessence interacting withdark or baryonic matter. We use a variational approach for relativistic fluidsto realize an effective description of matter fields at the Lagrangian level.The coupling is introduced directly in the action by considering a singlefunction mixing the dynamical degrees of freedom of the theory. The resultinggravitational field equations are derived by variations with respect to theindependent variables. New interesting phenomenology can be obtained at bothsmall scales, where new screening mechanisms for scalar fields can be realized,and large scales, where one finds an original and rich class of interactingquintessence models. The background cosmology of two of these models is studiedin detail using dynamical system techniques. We find a variety of interestingresults: for instance, these models contain dark energy dominated late timeattractors and scaling solutions, both with early time matter dominated epochsand a possible inflationary origin. In general this new approach provides thestarting point for future in depth studies on new interacting quintessencemodels.

Interacting quintessence from a variational approach Part I: algebraic couplings