Dark energy with zero pressure: Accelerated expansion and large scale structure in action-dependent Lagrangian theories

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We develop a cosmological model based on action-dependent Lagrangian theories. The main feature here is the nonconservation of the energy momentum tensor due to the nontrivial geometrical construction of the theory. We provide the basic set of equations necessary to study both the cosmological background expansion as well as the linear matter perturbation growth. We show that the simplest realization of the Universe as described by only one component is not viable as expected from the existing correspondence between this model and the case of viscous cosmological fluids. However, modeling the energy content of the Universe as composed by two pressureless fluids, i.e., one a typical cold dark matter fluid and the other a pressureless dark energy fluid which is responsible for driving the late-time acceleration expansion, is qualitatively compatible with observational data.