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A future measurement of cosmic microwave \mu-distortions by an experimentwith the specifications of PIXIE will provide an equivalent 3-sigma detectionof the running of running of the spectral index of scalar perturbations, \beta= d\alpha/dln(k), if \mu > 7.75 E-8, covering much of the PIXIE sensitivityrange. This corresponds to a resolution limit of \beta > 0.015 which isrelatively large given any presumption of slow roll, a result of the currenttight constraints on \alpha < 0 on CMB scales. We show that a detection of\beta at this level is in conflict with slow roll conditions if the primordialsignal can be distinguished from any post-inflationary contamination.

Scalar runnings and a test of slow roll from CMB distortions