Anisotropic non-gaussianity with noncommutative spacetime

TL;DR

This paper investigates how noncommutative spacetime affects inflationary perturbations, revealing anisotropic signatures in the power spectrum and bispectrum, with potential observational constraints from CMB data.

Contribution

It provides the first detailed calculation of two- and three-point functions in noncommutative inflation, highlighting anisotropic effects and scale-dependent non-Gaussianity.

Findings

Power spectrum and bispectrum are statistically anisotropic.

The bispectrum is modified by a phase factor from noncommutative parameters.

The non-linearity parameter $f_{NL}$ remains small and consistent with PLANCK bounds.

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 $f_{NL}$ 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 $f_{NL}$ 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.