Observational test of inflation in loop quantum cosmology

TL;DR

This paper investigates how loop quantum cosmology's inverse-volume corrections influence inflationary power spectra, deriving observational bounds and assessing compatibility of different inflation potentials with data.

Contribution

It provides explicit formulas for inflationary spectra in LQC including higher-order corrections and constrains quantum effects using observational data.

Findings

Inverse-volume corrections can cause large spectral runnings and power enhancements at large scales.

Quadratic inflation models remain compatible with data under LQC corrections.

Quartic inflation models are in tension with observational bounds.

Abstract

We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulae for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. Via a standard analysis, we place observational bounds on the inverse-volume quantum correction \delta ~ a^{- \sigma} (\sigma >0, $a$ is the scale factor) and the slow-roll parameter \epsilon_V for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on \delta for two pivot wavenumbers k_0 for several values of \delta. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on \delta (k_0) for given \sigma and k_0 are insensitive to the choice of the inflaton potentials.