Inflation and quantum cosmology

The paper starts with a discussion of the ''standard'' inflationary universe scenario and of some new trends in the theory of baryogenese and in the theory of galaxy formation. Stochastic approach to the investigation of inflationary universe is discussed as well and the results obtained within this approach are compared with the results obtained in the context of Euclidean quantum cosmology. It is shown that the universe containing at least one inflationary domain filled with a sufficiently big scalar field φ unceasingly produces inflationary domains of all possible types. In this scenario the universe, after inflation becomes divided into many exponentially large domains, inside which the laws of law energy physics and even the dimensionality of space-time may be different. Finally, the exciting possibilities related to the baby-universe theory are discussed. 80 refs