Accelerated expansion of an open universe, and string theory realizations

Recently, many works have tried to realize cosmological accelerated expansion in string theory models in the asymptotic regions of field space, with a typical scalar potential $V(\varphi)$ having an exponential fall-off $e^{-\gamma\, \varphi}$. Those attempts have been plagued by the fact that $V$ is too steep, namely $\gamma \geq 2/\sqrt{d-2}$ in a $d$-dimensional spacetime. We revisit the corresponding dynamical system for arbitrary $d$ and $\gamma$, and show that for an open universe ($k=-1$), there exists a new stable fixed point $P_1$ precisely if $\gamma > 2/\sqrt{d-2}$. Building on the recent work arXiv:2210.10813, we show in addition that cosmological solutions asymptoting to $P_1$ exhibit accelerated expansion in various fashions (semi-eternal, eternal, transient with parametrically controlled number of e-folds, or rollercoaster). We finally present realizations in string theory of these cosmological models with asymptotically accelerating solutions, for $d=4$ or $d=10$. We also show that these solutions do not admit a cosmological event horizon, and discuss the possibility of this being a generic feature of quantum gravity.