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Double Field Theory with matter and its cosmological application

The phase space formulation of Double Field Theory (DFT) indicates that statistical matter can be included in terms of (T-)duality multiplets. We propose the inclusion of a perfect fluid in the geometry of DFT through a generalized energy-momentum tensor written in terms of a DFT pressure, energy density and velocity. The latter is an $O(D,D)$ vector and satisfies two invariant constraints, in agreement with the on-shell constraints for the generalized momentum. We compute the conservation laws associated to the energy-momentum tensor considering general DFT backgrounds. Then we study cosmological backgrounds using a space-time split, and we find an expression for the DFT cosmological dynamics with the perfect fluid coupled. This proposal reproduces the equations of string cosmology upon parametrization of the DFT Einstein equations.