Eur. Phys. J. C 69, 521-529 (2010)
https://doi.org/10.1140/epjc/s10052-010-1421-4

CMB constraints on non-commutative geometry during inflation

Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand

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Received: 10 April 2010
Revised: 22 July 2010
Published online: 11 September 2010

Abstract

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.