Cosmology with a three-form field interacting with cold dark matter is considered. In particular, the mass of the dark matter particles is assumed to depend upon the amplitude of the three-form field invariant. In comparison to coupled scalar field quintessence, the new features include an effective pressure contribution to the field equations that manifests both in the background and perturbation level. The dynamics of the background is analyzed, and new scaling solutions are found. A simple example model leading to a de Sitter expansion without a potential is studied. The Newtonian limit of cosmological perturbations is derived, and it is deduced that the coupling can be very tightly constrained by the large-scale structure data. This is demonstrated with numerical solutions for a model with nontrivial coupling and a quadratic potential.
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