Implications of a running spectral index for slow roll inflation

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