  We present an study from PLANCK2013+WP+BAO:$\Lambda$CDM+$r$+$\alpha_s$ data,
where 49 slow roll inflationary potentials are tested, showing that the
theoretical value of the running provided by 48 of these potentials has a
deviation to the expected observational value larger than $1.6\sigma$, and its
modulus is smaller than the modulus of the expected observational one, what
disfavours these models at 94.5 \% of Confidence Level (C.L.), concluding from
these results that, inflationary cosmology may require multiple fields or a
breakdown of slow roll condition. This conclusion has drastically changed with
the last data provided by PLANCK2015 where the modulus of the expected
observational value of the running has been reduced one order, getting shorter
the distance to its theoretical value $1\sigma$ or more, what allows the
viability of the majority of the potentials disfavored by the running provided
by PLANCK2013 data. However if one takes into account the running of the
running, its theoretical value, which in the slow roll regime depends on the
slow roll parameters at third order, is incompatible with the expected
observational value provided by PLANCK2013 and PLANCK2015, disfavouring at 92.8
\% C.L. or more, 39 of the 49 slow roll potentials tested. Moreover, if one
restricts the number of e-folds to be between 30 and 80, then only two
potentials will survive to this test.
