Implications of a running spectral index for slow roll inflation

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We analyse the weak (2σ) evidence for a running spectral index seen in the three year WMAP data set and itsimplications for single field, slow roll inflation. We assume that the running is comparableto the central value found from the WMAP data analysis, and use the Hubble slow rollformalism to follow the evolution of the slow roll parameters. For all parameter choicesconsistent with a large, negative running, single field, slow roll inflation lasts less than 30e-folds after CMB scales leave the horizon. Thus, a definitive observation of a large negativerunning would imply that any inflationary phase requires multiple fields or thebreakdown of slow roll. Alternatively, if single field, slow roll inflation sourcesthe primordial fluctuations, we can expect the observed running to move muchcloser to zero as the CMB is measured more accurately at small angular scales.