# A Schrodinger formulation of Bianchi I scalar field cosmology

@article{DAmbroise2007ASF, title={A Schrodinger formulation of Bianchi I scalar field cosmology}, author={J. D’Ambroise}, journal={arXiv: High Energy Physics - Theory}, year={2007} }

We show that the Bianchi I Einstein field equations in a perfect fluid scalar field cosmology are equivalent to a linear Schrodinger equation. This is achieved through a special case of the recent FLRW Schrodinger-type formulation, and provides an alternate method of obtaining exact solutions of the Bianchi I equations.

#### 4 Citations

Scalar field exact solutions for non-flat FLRW cosmology: a technique from non-linear Schrödinger-type formulation

- Physics
- 2009

We report a method of solving for canonical scalar field exact solution in a non-flat FLRW universe with barotropic fluid using non-linear Schrödinger (NLS)-type formulation in comparison to the… Expand

Generalized EMP and nonlinear Schrodinger-type reformulations of some scalar field cosmological models

- Physics, Mathematics
- 2010

We show that Einstein's gravitational field equations for the Friedmann-Robertson-Lema\^itre-Walker (FRLW) and for two conformal versions of the Bianchi I and Bianchi V perfect fluid scalar field… Expand

Applications of Elliptic and Theta Functions to Friedmann-Robertson-Lemaitre-Walker Cosmology with Cosmological Constant

- Physics, Mathematics
- 2009

Elliptic functions are known to appear in many problems, applied and theoretical. However, a lesser known application is in the study of exact solutions to Einstein's gravitational field equations in… Expand

Comprehensive analysis of the symmetries and conservation laws of the geodesic equations for a particular string inspired FRLW solution

- Mathematics, Computer Science
- Commun. Nonlinear Sci. Numer. Simul.
- 2017

This paper is dedicated to a thorough investigation of the symmetries and conservation laws of the geodesic equations associated to a specific exact cosmological solution of a scalar-field potential which was originally motivated by six-dimensional Einstein-Maxwell theory. Expand

#### References

SHOWING 1-8 OF 8 REFERENCES

A non-linear Schrodinger type formulation of FLRW scalar field cosmology

- Physics
- 2006

We show that the Friedmann-Lemaitre-Robertson-Walker equations with scalar field and perfect fluid matter source are equivalent to a suitable non-linear Schrodinger type equation. This provides for… Expand

Ermakov-Pinney equation in scalar field cosmologies

- Physics, Mathematics
- 2002

It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the non-linear, Ermakov-Pinney equation. The general solution… Expand

Multiple and anisotropic inflation with exponential potentials

- Physics
- 1992

It is shown how the field equations for a self-interacting scalar field propagating in the Bianchi I spacetime can be expressed as a set of first-order non-linear partial differential equations.… Expand

A plane symmetric Bianchi type-I inflationary universe in general relativity

- Physics
- 2009

A plane symmetric homogeneous space-time in the presence of mass less scalar field with a flat potential is investigated. To get an inflationary universe, we have considered a flat region in which… Expand

A search for shape-invariant solvable potentials

- Mathematics
- 1989

The author investigates a simple method of constructing potentials which is related to the work of Bhattacharjie and Sudarshan (1962) and for which the Schrodinger equation can be solved in terms of… Expand

Derivation of the Raychaudhuri Equation

- Physics
- 2005

As a homage to A K Raychaudhuri, I derive in a straightforward way his famous equation and also indicate the problems he was last engaged in.

Bianchi I inflationary universe in general relativity

- Pramana -Journal of Physics
- 2002

Bianchi I inflationary universe in general relativity

- Pramana - Journal of Physics