General String Cosmologies at Order $\alpha'{}^{\,3}$

We compute the cosmological reduction of general string theories, including bosonic, heterotic and type II string theory to order $\alpha'^{3}$, i.e., with up to eight derivatives. To this end we refine recently introduced methods that allow one to bring the reduced theory in one dimension to a canonical form with only first-order time derivatives. The resulting theories are compatible with a continuous $O(d,d,\mathbb{R})$ invariance, which in turn fixes the B-field couplings.