Bounds on slow roll at the boundary of the landscape

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 ϕ 0 in an N -dimensional field space with V ( ϕ 0) > 0, there exists a path of monotonically decreasing potential energy to a point ϕ 1 within a path length ≲ 𝒪 (1), such that √(N)lnV(ϕ_1)/V(ϕ_0)≲ -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.