IJPAM: Volume 34, No. 1 (2007)

A NON-LINEAR SCHRÖDINGER TYPE FORMULATION
OF FLRW SCALAR FIELD COSMOLOGY

Jennie D'Ambroise$^1$, Floyd L. Williams$^2$
$^{1,2}$Department of Mathematics and Statistics
University of Massachusetts
Amherst, MA 01003, USA
$^1$e-mail: dambroise@math.umass.edu
$^2$e-mail: williams@math.umass.edu


Abstract.We show that the Friedmann-Lemaître-Robertson-Walker equations with scalar field and perfect fluid matter source are equivalent to a suitable non-linear Schrödinger type equation. This provides for an alternate method of obtaining exact solutions of the Einstein field equations for a homogeneous, isotropic universe.

Received: October 23, 2006

AMS Subject Classification: 83C05, 83C15

Key Words and Phrases: Einstein field equations, Friedmann-Lemaître-Robertson-Walker universe, scalar field, scale factor, perfect fluid, Ermakov-Milne-Pinney equation, non-linear Schrödinger equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 1