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Exact Solutions of the Cauchy Problem for the Friedman Equation

Authors
  • Kurianovich, E. A.
Type
Published Article
Journal
Theoretical and Mathematical Physics
Publisher
Springer-Verlag
Publication Date
Apr 01, 2019
Volume
199
Issue
1
Pages
604–620
Identifiers
DOI: 10.1134/S004057791904010X
Source
Springer Nature
Keywords
License
Yellow

Abstract

We reduce the cosmological Friedmann equation for a universe filled with a scalar field to a system of two first-order equations, one of which is an equation with separable variables. For this equation, we write exact solutions for a quadratic potential as a series in the helical and attractor domains and also for quite arbitrary potentials both in the neighborhood of a finite point and in a neighborhood of infinity. We prove the existence and uniqueness of classical solutions of the Cauchy problem of the Friedmann equation in certain cases and the presence of exactly two solutions in other cases.

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