SPACE, TIME AND FUNDAMENTAL INTERACTIONS

APPLICATION OF THE SCHRODINGER EQUATION IN EXACT SCALAR FIELD COSMOLOGY

Fomin I.V., Chervon S.V., Maharaj S.D.

We propose a new method of exact solutions construction for scalar field cosmology based on representation of the Einstein-Friedmann dynamic equations as Schr?odinger-like one. This representation allows one to compare the solutions of quantum-mechanical and cosmological problems. On the other hand, this approach makes it possible to use the well-known form-invariant transformations of the Schrodinger equation to generate exact cosmological solutions. As an example of the application of this method, the use of the Darboux transformations in scalar field cosmology is considered. On the other hand, the presented methods make it possible to generalize the obtained solutions to multi-field cosmological models.