A Note on Curvature Fluctuation of Noncommutative Inflation

TL;DR

This paper investigates how the choice of initial vacuum states, influenced by stringy spacetime uncertainty, affects the power spectrum of curvature fluctuations during power law inflation in noncommutative spacetime.

Contribution

It introduces a specific vacuum choice based on spacetime noncommutativity and calculates its impact on the curvature fluctuation spectrum.

Findings

The initial vacuum choice significantly alters the power spectrum.

The effect is analyzed up to the leading order of noncommutativity parameter.

Results highlight the importance of vacuum selection in noncommutative inflation models.

Abstract

An elegant approach, which incorporates the effect of the stringy spacetime uncertainty relation, to calculate power spectra of fluctuations during inflation has been suggested by Brandenberger and Ho. In this approach, one of important features is the appearance of an upper bound on the comoving momentum $k$, at which the stringy spacetime uncertainty relation is saturated. As a result, the time-dependent upper bound leads us to choose naturally a set of initial vacua for each mode, in which the stringy uncertainty relation is saturated. In this note, with that set of vacua we calculate power spectrum of curvature fluctuation for a power law inflation, up to the leading order of a parameter describing the spacetime noncommutativity. It turns out that this choice of initial vacuum has a significant effect on the power spectrum of fluctuations.