  In string theory the closed-string massless NS-NS sector forms a multiplet of
$\mathbf{O}(D,D)$ symmetry. This suggests a specific modification to General
Relativity in which the entire NS-NS sector is promoted to stringy graviton
fields. Imposing off-shell $\mathbf{O}(D,D)$ symmetry fixes the correct
couplings to other matter fields and the Einstein field equations are enriched
to comprise $D^{2}+1$ components, dubbed recently as the Einstein Double Field
Equations. Here we explore the cosmological implications of this framework. We
derive the most general homogeneous and isotropic ansatzes for both stringy
graviton fields and the $\mathbf{O}(D,D)$-covariant energy-momentum tensor.
Crucially, the former admits space-filling magnetic $H$-flux. Substituting them
into the Einstein Double Field Equations, we obtain the $\mathbf{O}(D,D)$
completion of the Friedmann equations along with a generalized continuity
equation. We discuss how solutions in this framework may be characterized by
two equation-of-state parameters, $w$ and $\lambda$, where the latter
characterizes the relative intensities of scalar and tensor forces. When
$\lambda+3w=1$, the dilaton remains constant throughout the cosmological
evolution, and one recovers the standard Friedmann equations for generic matter
content (i.e. for any $w$). We further point out that, in contrast to General
Relativity, neither an $\mathbf{O}(D,D)$-symmetric cosmological constant nor a
scalar field with positive energy density gives rise to a de Sitter solution.
