Noncommutative spacetime geometry and one-loop effects in primordial cosmology

TL;DR

This paper investigates how noncommutative spacetime geometry influences one-loop quantum corrections during inflation, revealing momentum-dependent, anisotropic effects that could imprint nonlocal signatures on the primordial cosmological spectrum.

Contribution

It introduces a model of noncommutative spacetime during inflation and analyzes its impact on quantum corrections to the primordial power spectrum, highlighting UV/IR mixing effects.

Findings

One-loop corrections become momentum-dependent and anisotropic.

Vacuum fluctuations source curvature fluctuations beyond horizon scales.

Noncommutative parameters induce observable anisotropy in the primordial spectrum.

Abstract

We study the effect of noncommutative spacetime geometry on one-loop corrections to the primordial curvature two-point function, arising from various forms of massless spectator matter fields interacting gravitationally with the inflaton. After deforming the algebra of functions on the inflationary background to a spatially noncommutative one, we find that this induces momentum-dependent corrections to one-loop terms which imply that the vacuum fluctuation of the energy-momentum tensor sources that of the curvature fluctuation even for distances beyond horizon scales. The one-loop corrections break spatial isotropy by being functions of the noncommutative parameters lying in the tranverse plane while reducing smoothly to the commutative limit. This furnishes an example of how UV/IR mixing manifests itself in the context of noncommutative field theories defined on inflationary backgrounds, and demonstrates how in principle, the primordial spectrum could carry a signature of nonlocality and anisotropy in the setting of noncommutative spacetime geometry.