EMP and linear Schrodinger models for a conformally Bianchi I cosmology

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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Scientific paper

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.

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