Non-commutative Power-law Inflation: Mode Equation and Spectra Index

TL;DR

This paper investigates how non-commutative spacetime effects influence primordial perturbations during power-law inflation, providing analytical mode solutions and comparing predictions with WMAP data to estimate key parameters.

Contribution

It introduces a new approximation for mode functions in non-commutative power-law inflation and assesses the impact of spacetime non-commutativity on the primordial power spectrum.

Findings

Non-commutativity causes small corrections to the primordial power spectrum.

The model's parameters are consistent with WMAP observations.

Estimated string scale is approximately 2.0×10^{-29} cm.

Abstract

Following an elegant approach that merge the effects of the stringy spacetime uncertainty relation into primordial perturbations suggested by Brandenberger and Ho, we show the mode equation up to the first order of non-commutative parameter. A new approximation is provided to calculate the mode functions analytically in the non-commutative power-law inflation models. It turns out that non-commutativity of spacetime can provide small corrections to the power spectrum of primordial fluctuations as the first-year results of WMAP indicate. Moreover, using the WMAP data, we obtain the value of expansion parameter, non-commutative parameter and find the approximation is viable. In addition, we determined the string scale $l_s \simeq 2.0\times 10^{-29}{cm}$.