Non-linear stability of ${\alpha }^{\mathrm{\prime }}$-corrected Friedmann equations

We study the non-linear stability of fixed-point solutions to the ${\alpha }^{\mathrm{\prime }}$-exact equations from O$(d,d)$ invariant cosmology, with and without matter perturbations. Previous non-linear analysis in the literature is revisited, and its compatibility with known linear perturbation results is shown. Some formal aspects of cosmological perturbations in duality invariant cosmology are discussed, and we show the existence of time-reparameterization invariant variables for perturbations.