Observational test of inflation in loop quantum cosmology

We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (I,QC). 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 fort:fluky 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 proportional to 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 a and k(0) are insensitive to the choice of the inflaton potentials.