Relativistic cosmology with quantum corrections

Homogeneous isotropic, anisotropic and inhomogeneous cosmological models are studied using Einstein's general relativity with quantum corrections in field theoretical approximation. In particular we discuss coherent scalar fields and curvature squared terms in the gravitational Lagrangian. The conformal equivalence of the field equations of fourth order to general relativity with a scalar field as source is an example of the geometrization of a matter field. The semiclassical quantum corrections of the scalar fields can avoid the intial cosmological singularity and they lead to an inflationary evolution stage as transient attractor. The review provides new points of view on questions like the probability of the inflationary stage and the question of mechanisms for multiple inflation. (orig.)