CMB constraints on non-commutative geometry during inflation.

Karwan, Khamphee

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 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 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 is estimated to be less than 10 cm at 99.7% confidence level.

GEOMETRY; POWER (Mechanics); ANISOTROPY; ASTRONOMICAL perturbation; CELESTIAL mechanics

European Physical Journal C -- Particles & Fields, 2010, Vol 69, Issue 3/4, p521

1434-6044

Academic Journal

10.1140/epjc/s10052-010-1421-4