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

The twilight of the single field slow rolling inflaton