CMB constraints on noncommutative geometry during inflation
  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
L_s 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 L_s 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 L_s is estimated to be less than 10^{-27} cm at
99.7% confidence level.
