CMB constraints on noncommutative geometry during inflation

TL;DR

This paper explores how noncommutative spacetime during inflation affects the primordial power spectrum and CMB anisotropies, setting upper bounds on the noncommutative length scale using WMAP data.

Contribution

It introduces a model linking spacetime noncommutativity to primordial perturbations and constrains the noncommutative length scale using observational CMB data.

Findings

Upper bound for noncommutative length scale L_s < 10^{-27} cm

Deviation from rotational invariance depends on L_s, not sound speed

Constraints are consistent with inflationary cosmology

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 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.