Exponential Quintessence: curved, steep and stringy?

Understand

We explore the possibility that our universe's current accelerated expansion is explained by a quintessence model with an exponential scalar potential, $V =V_0\, e^{-\lambda\, \phi}$, keeping an eye towards $\lambda \geq \sqrt{2}$ and an open universe, favorable to a string theory realisation and with no cosmological horizon.

• We work out the full cosmology of the model, including matter, radiation, and optionally negative spatial curvature, for all $\lambda>0$, performing an extensive analysis of the dynamical system and its phase space.
• The minimal physical requirements of a past epoch of radiation domination and an accelerated expansion today lead to an upper bound $\lambda \lesssim \sqrt{3}$, which is driven slightly up in the presence of observationally allowed spatial curvature.
• Cosmological solutions start universally in a kination epoch, go through radiation and matter dominated phases and enter an epoch of acceleration, which is only transient for $\lambda>\sqrt{2}$.