  Higher-derivative corrections to cosmological effective actions in string
theory are largely constrained by T-duality, but have been computed hitherto
only to the first few orders in the string scale $\alpha'$. The functional
renormalization group, in conjunction with the strong constraints imposed by
T-duality, allows to derive cosmological effective actions to all orders in
$\alpha'$ while avoiding "truncations" of the theory space. We show that the
resulting higher-derivative $\alpha'$-corrections forbid the existence of de
Sitter vacua, at least in regimes where string-loop corrections can be
neglected. Our findings thus support the implications of the no-de Sitter
swampland conjecture in the presence of all-order effects in $\alpha'$.
