Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory

The low-energy limit of string theory contains additional gravitational degrees of freedom, a skew-symmetric tensor $B$-field and a scalar dilaton, that are not present in general relativity. Together with the metric, these three fields are naturally embedded in the $\mathbf{O}(D,D)$-symmetric framework of double field theory. The $\mathbf{O}(D,D)$ symmetry uniquely prescribes the interactions between the extended gravitational sector and other matter, leading to novel features beyond conventional string cosmology. In this work we present the equations of motion for linear perturbations around $\mathbf{O}(D,D)$ string cosmological backgrounds in $D=4$ under a scalar-vector-tensor decomposition. We obtain analytic solutions in the superhorizon limit for scalar perturbations around various homogeneous and isotropic background solutions, including some candidate models for bouncing cosmologies. The generalized energy-momentum tensor includes source terms for the $B$-field and dilaton, and we show how the resulting generalized conservation laws modify the conditions for conservation of curvature perturbations.