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Inflationary power spectra with quantum holonomy corrections

In this paper we study slow-roll inflation with holonomy corrections from loop quantum cosmology. Both tensor and scalar power spectra of primordial perturbations are computed up to the first order in slow-roll parameters and $V/ρ_{c}$, where $V$ is a potential of the scalar field and $ρ_{c}$ is a critical energy density (expected to be of the order of the Planck energy density). Possible normalizations of modes at short scales are discussed. In case the normalization is performed with use of the Wronskian condition applied to adiabatic vacuum, the tensor and scalar spectral indices are not quantum corrected in the leading order. However, by choosing an alternative method of normalization one can obtain quantum corrections in the leading order. Furthermore, we show that the holonomy-corrected equation of motion for tensor modes can be derived from an effective background metric. This allows us to prove that the Wronskian normalization condition for the tensor modes preserves the classical form.