  In this paper we operate under the assumption that no tensors from inflation
will be measured in the future by the dedicated experiments and argue that,
while for single-field slow-roll models of inflation the running of the
spectral index will be hard to be detected, in multi-field models the running
can be large due to its strong correlation with non-Gaussianity. A detection of
the running might therefore be related to the presence of more than one active
scalar degree of freedom during inflation.
