On Cosmologies and Vacua Driven by Tension and Curvatures

We investigate the effects of the exponential potentials typical of non-supersymmetric strings in cosmologies whose spatial and internal slices are maximally symmetric spaces with curvatures labeled by a pair of integers $k$ and $k^{\mathrm{\prime }}$ ($=\pm 1$). We classify the solutions according to their singularity structure and asymptotic behavior and present a semi-quantitative picture of the generic dynamics in the physically most relevant cases with flat spatial slices. The analysis relies on exact solutions emerging when one of the effects dominates, special solutions arising when two or more effects are comparable, scaling asymptotics, and some numerical tests.