Accelerated expansion of an open universe, and string theory realizations

Abstract: 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.