Cosmological Chameleons, String Theory and the Swampland

We study a scenario with a transient phase of cosmological acceleration that could potentially be realized in asymptotic corners of String Theory moduli space. A very steep scalar potential is temporarily stabilized by the effect of a nonzero density of heavy states, leading to acceleration, in what amounts to a cosmological version of the Chameleon mechanism. The density of heavy states is diluted by cosmological expansion, weakening their effect. After roughly one $e$-fold their effect can no longer stabilize the potential, and the accelerating phase ends. We also study a scenario where there is no potential and the transient acceleration is achieved by the counterbalancing effects of light and heavy towers of states. In both cases we show that it is not possible to obtain more than $\mathcal{O}(1)$ $e$-folds without transplanckian field excursions. We also discuss the general EFT constraints on these models and explore a number of first attempts at concrete embeddings of the scenario in String Theory. These all turn out to face significant challenges.