  The massless fields in the universal NS-NS sector of string theory form $O(D,
D)$ multiplets of Double Field Theory, which is a theory that provides a
T-duality covariant formulation of supergravity, leading to a stringy
modification of General Relativity. In this framework, it is possible to write
down the extensions of the Einstein field equations and the Friedmann equations
in such a way that the coupling of gravitational and matter sectors is dictated
by the $O(D, D)$ symmetry universally. In this paper, we obtain the autonomous
form of the $O(D, D)$-complete Friedmann equations, find the critical points
and perform their stability analysis. We also include the phase portraits of
the system. Cosmologically interesting cases of scalar field, radiation, and
matter are separately considered and compared with the Chameleon models in a
similar setting. Accelerating phases and the conditions for their existence are
also given for such cases.
