Running Spectral Index in Noncommutative Inflation and WMAP Three Year Results

A model independent analysis shows that the running of the spectral index of the three year WMAP results can be nicely realized in noncommutative inflation. We also reexamine some concrete noncommutative inflation models. We find that a large tensor-scalar ratio is required, corresponding to a low number of e-folds before the end of inflation in some simple models. An epoch of accelerated expansion in the early universe, inflation, dynamically resolves many cosmological puzzles such as homogeneity, isotropy and flatness of the universe [1], and generates superhorizon fluctuations without appealing to fine-tuned initial setups. These fluctuations become classical after crossing out the Hubble horizon. During the deceleration phase after inflation they re-enter the horizon, and seed the matter and the radiation fluctuations observed in the universe. The anisotropy in CMB encodes the very important information for inflation. The ΛCDM model remains an excellent fit to the three years WMAP data and other astronomical data [2]. In the simplest models for the structure formation, a scale-invariant spectrum of the primordial power spectrum is no longer a good fit to the three year data, implying that inflation must be dynamic. Some simple inflation models are already ruled out [2,3]. The deficit of power in low mulitipoles of the angular power spectrum in the first year results of WMAP is not preferred by the three years results anymore. Even though allowing for a running spectral index slightly improves the fit to the WMAP data, the improvement in the fit is not significant enough to require this new parameter. However, it is important that a running index still survives the three year data together with other sets of data. Since it is hard to realize a large running in the usual slow-roll inflation models [4], we hope that future experiments will confirm a running spectral index and thus open a new window into the physics of the first moments of the big bang and provides some clues into trans-Planckian physics. Noncommutative spacetime naturally emerges in string theory [5], which implies a new uncertainty relation ∆t p ∆x p ≥ l 2 s , (1) where t p and x p are the physical time and space, l s is uncertainty length scale or string scale in string theory. Constructing a realistic inflation model in noncommutative spacetime is still an open question. Motivated by the first year WMAP resuls, we found in [7-9] that a toy …