Exact solutions for a big bounce in loop quantum cosmology

In this paper we study the flat (k=0) cosmological Friedmann-Robertson-Walker model with holonomy corrections of loop quantum gravity. The considered universe contains a massless scalar field and the cosmological constant Lambda. We find analytical solutions for this model in different configurations and investigate its dynamical behavior in the whole phase space. Such an approach might be significant e.g. as a phenomenological reference for a further, fully quantum treatment. We show the explicit influence of Lambda on the qualitative and quantitative character of solutions. Even in the case of positive Lambda the oscillating solutions without the initial and final singularity appear as a generic case for some quantization schemes.