Strong multifield slowroll condition and spiral inflation

We point out the existing confusion about the slowroll parameters and conditions for multifield inflation. If one requires the fields to roll down the gradient flow, we find that only articles adopting the Hubble slowroll expansion are on the right track, and a correct condition can be found in a recent book by Liddle and Lyth [The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure (Cambridge University Press, Cambridge, England, 2009)]. We further analyze this condition and show that the gradient flow requirement is stronger than just asking for a slowly changing, quasi-de Sitter solution. Therefore, it is possible to have a multifield slowroll model that does not follow the gradient flow. Consequently, it no longer requires the gradient to be small. It even bypasses the first slowroll condition and some related no-go theorems from string theory. We provide the "spiral inflation'' as a generic blueprint of such an inflation model and show that it relies on a monodromy locus, a common structure in string theory effective potentials.