Cosmological Perturbations in Double Field Theory

We explore perturbative double field theory about time-dependent (cosmological) backgrounds to cubic order. To this order the theory is consistent in a weakly constrained sense, so that for a toroidal geometry it encodes both momentum and genuine winding modes. We give a self-contained discussion of the consistency problems and their resolution, including the role of cocycle factors and the $O(d,d,\mathbb{Z})$ duality. Finally, as a first step toward the computation of cosmological correlation functions, we propose a generalized scalar-vector-tensor decomposition and use it to construct gauge invariant generalized Bardeen variables. Compared to standard cosmology there are fewer tensor modes but more vector and scalar modes.