Inflationary power spectra with quantum holonomy corrections

Abstract

In this paper we study slow-roll inflation with holonomy correctionsfrom loop quantum cosmology. It was previously shown that, in the Planckepoch, these corrections lead to such effects as singularity avoidance, metricsignature change and a state of silence. Here, we consider holonomy correctionsaffecting the phase of cosmic inflation, which takes place away from the Planckepoch. Both tensor and scalar power spectra of primordial inflationaryperturbations are computed up to the first order in slow-roll parameters andV/ρc, where V is a potential of the scalar field and ρc is acritical energy density (expected to be of the order of the Planck energy density).Possible normalizations of modes at short scales are discussed. In case thenormalization is performed with use of the Wronskian condition applied toadiabatic vacuum, the tensor and scalar spectral indices are not quantumcorrected in the leading order. However, by choosing an alternative method ofnormalization one can obtain quantum corrections in the leading order.Furthermore, we show that the holonomy-corrected equations of motion fortensor and scalar modes can be derived based on effective background metrics.This allows us to show that the classical Wronskian normalization conditionis well defined for the cosmological perturbations with holonomy corrections.