Testing the inflationary slow-roll condition with tensor modes

A major goal of modern cosmology is the detection of B-modes in the cosmic microwave background polarization originated from primordial gravitational waves. Their detection not only could provide substantial evidence for primordial inflation but also could shed light on its physical nature. Under the assumption of single-field slow-roll inflation, a set of conditions exist for the scalar and tensor parameters. In particular, given a constraint on the scalar spectral index ns, its running αs, its running of running βs, and the tensor-to-scalar ratio r, constraints can be derived on the tensor spectral index nt, its running αt, its running of running βt, and its running of running of running γt. Using current bounds from the Planck 2015 and BICEP2 datasets and under the slow condition we found the following constraints at 95% C.L.: nt>-0.0157, αt=-0.00018-0.00024+0.00019, βt=0.00004-0.00013+0.00022, and γt=0.00017-0.00019+0.00040. Future measurements of the tensor spectrum could therefore be used to test these bounds and the slow-roll condition.