Possible observational effects of loop quantum cosmology

In this paper, we consider realistic model of inflation embedded in the framework of loop quantum cosmology. Phase of inflation is preceded here by the phase of a quantum bounce. We show how parameters of inflation depend on the initial conditions established in the contracting, prebounce phase. Our investigations indicate that phase of the bounce easily sets proper initial conditions for the inflation. Subsequently, we study observational effects that might arise due to the quantum gravitational modifications. We perform preliminary observational constraints for the Barbero-Immirzi parameter gamma, critical density rho(c), and parameter lambda. In the next step, we study effects on power spectrum of perturbations. We calculate spectrum of perturbations from the bounce and from the joined bounce + inflation phase. Based on these studies, we indicate a possible way to relate quantum cosmological models with the astronomical observations. Using the Sachs-Wolfe approximation, we calculate the spectrum of the superhorizontal CMB anisotropies. We show that quantum cosmological effects can, in the natural way, explain suppression of the low CMB multipoles. We show that fine-tuning is not required here, and the model is consistent with observations. We also analyze other possible probes of the quantum cosmologies and discuss perspectives of their implementation.