  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.
