Quantum cosmology from three different perspectives

Our review is devoted to three promising research lines in quantum cosmology and the physicsof the early universe. The nonperturbative renormalization programme is making encouraging progress that we here assess from the point of view of cosmological applications: Lagrangian and Hamiltonian form of pure gravity with variable G and Λ; power-law inflation for pure gravity; an accelerating universe without dark energy. In perturbative quantum cosmology, on the other hand, diffeomorphism-invariant boundary conditions lead naturally to a singularity-free one-loop wavefunction of the Universe. Last, but not least, in the braneworld picture one discovers the novel concept of cosmological wave function of the bulk space-time. Its impact on quantum cosmologyand singularity avoidance is still, to a large extent, unexplored.