CMB constraints on noncommutative geometry during inflation
Abstract
We investigate the primordial power spectrum of the density perturbations based on the assumption that spacetime is noncommutative in the early stage of inflation. Due to the spacetime noncommutativity, the primordial power spectrum can lose rotational invariance. Using the k-inflation model and slow-roll approximation, we show that the deviation from rotational invariance of the primordial power spectrum depends on the size of noncommutative length scale Ls but not on sound speed. We constrain the contributions from the spacetime noncommutativity to the covariance matrix for the harmonic coefficients of the CMB anisotropies using five-year WMAP CMB maps. We find that the upper bound for Ls depends on the product of sound speed and slow-roll parameter. Estimating this product using cosmological parameters from the five-year WMAP results, the upper bound for Ls is estimated to be less than 10-27 cm at 99.7% confidence level.