Field-space curvature and cosmic acceleration

In this project, we will study late-time solutions of the Friedmann equations in which the universe expansion is driven by a scalar sector with kinetic and potential exponential couplings. This represents a topic of great interest in string compactifications because, for solutions running towards the field space boundary, scalar potentials are expected to be steep enough to prevent the formation of a cosmic horizon, if the field space is flat. However, in the presence of curvature -- which is in fact expected, in string compactifications --, steep potentials are still compatible with accelerating solutions. Mathematically, we will formulate the problem in terms of an autonomous system of first-order differential equations, find critical points and determine their stability properties. The goal is to formulate sharp criteria for late-time cosmic acceleration in multi-field axion-dilaton models.