EMP and linear Schrodinger models for a conformally Bianchi I cosmology
General Relativity and Quantum Cosmology
2008-09-30 v1
Abstract
Using a conformal version of the Bianchi I metric and a perfect fluid energy-momentum tensor, we show that the resulting Einstein field equations are equivalent to a generalized Ermakov-Milne-Pinney equation. Using a transformation analogous to the known correspondence between the classical EMP and a linear Schr\"odinger equation, we then construct the linear Schr\"odinger formulation for this cosmological model. Also, a note is included to show the extra term that arises when the energy-momentum tensor is taken to include a second term in addition to the scalar field.
Cite
@article{arxiv.0809.4817,
title = {EMP and linear Schrodinger models for a conformally Bianchi I cosmology},
author = {Jennie D'Ambroise},
journal= {arXiv preprint arXiv:0809.4817},
year = {2008}
}