Abstract
We study single field inflation in noncommutative spacetime and compute two-point and three-point correlation functions for the curvature perturbation. We find that both power spectrum and bispectrum for comoving curvature perturbation are statistically anisotropic and the bispectrum is also modified by a phase factor depending upon the noncommutative parameters. The non-linearity parameter fNL is small for small statistical anisotropic corrections to the bispectrum coming from the noncommutative geometry and is consistent with the recent PLANCK bounds. There is a scale dependence of fNL due to the noncommutative spacetime which is different from the standard single field inflation models and statistically anisotropic vector field inflation models. Deviations from statistical isotropy of CMB, observed by PLANCK can tightly constraint the effects due to noncommutative geometry on power spectrum and bispectrum.
Highlights
Inflation [1] solves the various puzzles of the Big-Bang theory, but it provides seeds for the temperature anisotropy of the cosmic microwave background (CMB) radiation and structures in the universe
The non-gaussianity in CMB is described in terms of the angular three-point correlation functions in harmonic space called as ”angular bispectrum”, which is related to the threedimensional bispectrum of the primordial curvature perturbations defined as [39, 40]
Detection of primordial non-gaussianity in the CMB anisotropy and large scale structure is the main challenge of current and future observations and it can play an important role in discriminating various models of inflation
Summary
Inflation [1] solves the various puzzles of the Big-Bang theory, but it provides seeds for the temperature anisotropy of the cosmic microwave background (CMB) radiation and structures in the universe. In this paper we compute the three-point correlation functions of the curvature perturbation and the non-linearity parameter fNL determining the primordial non-gaussianity using the noncommutative quantum field theories related to deformed Poincare symmetry [14]. In this approach of noncommutative geometry quantum fields follow twisted statistics, as implied by the deformed Poincare symmetry in quantum theories.
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