Noncommutative Decrumpling Inflation and Running of the Spectral Index

TL;DR

This paper introduces a novel inflation model incorporating noncommutative geometry and variable spatial dimensions, analyzing their effects on the spectral index and its running, with findings indicating the dominant influence of dimension variability.

Contribution

It presents the first detailed study of noncommutative decrumpling inflation, combining noncommutative geometry with time-varying spatial dimensions to analyze cosmological perturbations.

Findings

Effects of noncommutative geometry are smaller than those of variable spatial dimensions.

Spectral index and running are significantly influenced by the time variability of dimensions.

Comparison with standard slow-roll inflation shows distinct modifications due to the new model.

Abstract

We present a new inflation model, known as noncommutative decrumpling inflation, in which space has noncommutative geometry with time variability of the number of spatial dimensions. Within the framework of noncommutative decrumpling inflation, we compute both the spectral index and its running. Our results show that the effects of both time variability of the number of spatial dimensions and noncommutative geometry on the spectral index and its running. Two classes of examples have been studied and comparisons made with the standard slow-roll formulae. We conclude that the effects of noncommutative geometry on the spectral index and its running are much smaller than the effects of time variability of spatial dimensions.