Second-order corrections to noncommutative spacetime inflation

TL;DR

This paper explores how second-order noncommutative spacetime corrections influence inflationary power spectra, revealing effects that could align theoretical predictions with recent observational data.

Contribution

It introduces second-order noncommutative corrections to inflationary power spectra using slow-roll expansion, highlighting their impact on spectral indices and compatibility with WMAP data.

Findings

Noncommutative corrections modify the power spectrum and spectral index.

Higher-order corrections can compensate for losses in the commutative case.

Negative running spectral index aligns with recent WMAP observations.

Abstract

We investigate how the uncertainty of noncommutative spacetime affects on inflation. For this purpose, the noncommutative parameter $\mu_0$ is taken to be a zeroth order slow-roll parameter. We calculate the noncommutative power spectrum up to second order using the slow-roll expansion. We find corrections arisen from a change of the pivot scale and the presence of a variable noncommutative parameter, when comparing with the commutative power spectrum. The power-law inflation is chosen to obtain explicit forms for the power spectrum, spectral index, and running spectral index. In cases of the power spectrum and spectral index, the noncommutative effect of higher-order corrections compensates for a loss of higher-order corrections in the commutative case. However, for the running spectral index, all higher-order corrections to the commutative case always provide negative spectral indexes, which could explain the recent WMAP data.