Noncommutative Spacetime, Stringy Spacetime Uncertainty Principle, and Density Fluctuations

TL;DR

This paper introduces a noncommutative spacetime model consistent with string theory principles, analyzing its impact on cosmological fluctuations and revealing a scale-invariant spectrum under exponential expansion.

Contribution

It proposes a novel noncommutative spacetime framework that preserves symmetries and studies its effects on metric perturbations in cosmology.

Findings

Spectral index differs from commutative spacetime in the infrared region.

In exponential expansion, the spectrum is scale-invariant.

The magnitude of fluctuations depends on the Hubble constant relative to the string scale.

Abstract

We propose a variation of spacetime noncommutative field theory to realize the stringy spacetime uncertainty relation without breaking any of the global symmetries of the homogeneous isotropic universe. We study the spectrum of metric perturbations in this model for a wide class of accelerating background cosmologies. Spacetime noncommutativity leads to a coupling between the fluctuation modes and the background cosmology which is nonlocal in time. For each mode, there is a critical time at which the spacetime uncertainty relation is saturated. This is the time when the mode is generated. These effects lead to a spectrum of fluctuations whose spectral index is different from what is obtained for commutative spacetime in the infrared region, but is unchanged in the ultraviolet region. In the special case of an exponentially expanding background, we find a scale-invariant spectrum. but with a different magnitude than in the context of commutative spacetime if the Hubble constant is above the string scale.