Abstract
The three-year WMAP (Wilkinson microwave anisotropy probe) data imply not only anegative running of the spectral index with large absolute value, but also a largepositive running of the running of the spectral index with the order of magnitude10−2. We calculate the running of the running in the usual inflation modeland the non-commutative inflation model. A large tensor–scalar ratior≥1.23 is needed in order to fit the WMAP data in the non-commutative inflation model, whichroughly saturates the observational upper bound on it.
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