Detecting quantum gravitational effects of loop quantum cosmology in the
  early universe?
  We derive the primordial power spectra and spectral indexes of the density
fluctuations and gravitational waves in the framework of loop quantum cosmology
(LQC) with holonomy and inverse-volume corrections, by using the uniform
asymptotic approximation method to its third-order, at which the upper error
bounds are $\lesssim 0.15\%$, and accurate enough for the current and
forthcoming cosmological observations. Then, using the Planck, BAO and SN data
we obtain the tightest constraints on quantum gravitational effects from LQC
corrections, and find that such effects could be well within the detection of
the current and forthcoming cosmological observations.
