We study the matter-coupled equations of motion for cosmological NS massless fields including all alpha' corrections in an O(d, d) duality invariant approach, with emphasis on the Kalb-Ramond two-form field B-(2) and its source. Solutions for the vacuum and matter cases are found and the corresponding Einstein frame cosmologies are discussed. We also show that the ansatz for B-(2) required by the duality invariant framework implies that the two-form is non-isotropic.