Noncommutative spacetime effect on the slow-roll period of inflation

TL;DR

This paper investigates how noncommutative spacetime modifies the inflationary power spectrum, revealing that the noncommutative parameter suppresses the spectrum and can be treated as a slow-roll parameter.

Contribution

It provides an explicit form of the noncommutative power spectrum during inflation, including the effects of a variable noncommutative parameter, expanding understanding of quantum spacetime effects.

Findings

Noncommutative parameter suppresses the power spectrum.

Power spectrum explicitly depends on the noncommutative parameter $$.

Noncommutative effects can be incorporated as a zeroth order slow-roll parameter.

Abstract

We study how the noncommutative spacetime affects on inflation. First we obtain the noncommutative power spectrum of the curvature perturbations produced during inflation in the slow-roll approximation. This is the explicit $k$-dependent power spectrum up to first order in slow-roll parameters $\epsilon_1 \delta_1$ including the noncommutative parameter $\mu$. In order to test the role of $\mu$ further, we calculate the noncommutative power spectrum using the slow-roll expansion. We find corrections which arise from the change of pivot scale and a noncommutative parameter with $\mu\not=$ constant. It turns out that the noncommutative parameter $\mu$ could be considered as a zeroth order slow-roll parameter and the noncommutative spacetime effect suppresses the power spectrum.