Observational constraints on loop quantum cosmology
  In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections. 
Martin Bojowald, Gianluca Calcagni, Shinji Tsujikawa
astro-ph.CO gr-qc hep-ph hep-th