  The spectral index of scalar perturbations is an important observable that
allows us to learn about inflationary physics. In particular, a detection of a
significant deviation from a constant spectral index could enable us to rule
out the simplest class of inflation models. We investigate whether future
observations could rule out canonical single-field slow-roll inflation given
the parameters allowed by current observational constraints. We find that
future measurements of a constant running (or running of the running) of the
spectral index over currently available scales are unlikely to achieve this.
However, there remains a large region of parameter space (especially when
considering the running of the running) for falsifying the assumed class of
slow-roll models if future observations accurately constrain a much wider range
of scales.
