Bounds on Slow Roll at the Boundary of the Landscape

Abstract

We present strong evidence that the tree level slow roll bounds of arXiv:1807.05193 and arXiv:1810.05506 are valid, even when the tachyon has overlap with the volume of the cycle wrapped by the orientifold. This extends our previous results in the volume-dilaton subspace to a semi-universal modulus. Emboldened by this and other observations, we investigate what it means to have a bound on (generalized) slow roll in a multi-field landscape. We argue that for $any$ point ${\varphi }_0$ in an $N$-dimensional field space with $V({\varphi }_0)>0$, there exists a path of monotonically decreasing potential energy to a point ${\varphi }_1$ within a path length $\lesssim \mathcal{O}(1)$, such that $\sqrt{N}\ln \frac{V({\varphi }_1)}{V({\varphi }_0)}\lesssim -\mathcal{O}(1)$. The previous de Sitter swampland bounds are specific ways to realize this stringent non-local constraint on field space, but we show that it also incorporates (for example) the scenario where both slow roll parameters are intermediate-valued and the Universe undergoes a small number of e-folds, as in the Type IIA set up of arXiv:1310.8300. Our observations are in the context of tree level constructions, so we take the conservative viewpoint that it is a characterization of the classical "boundary" of the string landscape. To emphasize this, we argue that these bounds can be viewed as a type of Dine-Seiberg statement.

arXiv commentv4: one more reference

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