New classes of exact solutions in inflationary cosmology

The problem of determining a representation of the self-interaction potential in the form of a time dependence of the field potential energy which admits the existence of an inflationary regime and the transition of evolution to a Friedmann regime of asymptotic expansion is investigated within a cosmological model with a self-interacting scalar field. A variational formulation of the slow-roll concept is introduced, and, on the basis thereof, an exact solution is constructed for the evolution of the scale factor and the form of the self-interaction potential. A method based on representing the Einstein equations in the form of a linear second-order equation is developed for constructing and analyzing exact cosmological solutions of these equations. Selected types of potentials and the corresponding evolutions of the universe are investigated. Zh. éksp. Teor. Fiz. 114, 406–417 (August 1998)