Lessons from the running of the tensor-to-scalar ratio

We derive a simple consistency relation from the running of the tensor-to-scalar ratio. This new relation is first order in the slow-roll approximation. While for single field models we can obtain what can be found by using other observables, multifield cases in general give nontrivial contributions dependent on the geometry of the field space and the inflationary dynamics, which can be probed observationally from this relation. The running of the tensor-to-scalar ratio may be detected by direct laser interferometer experiments.