CMB constraints on non-commutative geometry during inflation
Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand
Revised: 22 July 2010
Published online: 11 September 2010
We investigate the primordial power spectrum of the density perturbations based on the assumption that space is non-commutative in the early stage of inflation, and constrain the contribution from non-commutative geometry using CMB data. Due to the non-commutative geometry, 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 non-commutative length scale L s but not on sound speed. We constrain the contributions from the non-commutative geometry to the covariance matrix of 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.
© Springer-Verlag / Società Italiana di Fisica, 2010