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arXiv · 2401.05775

Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization

Andronikos Paliathanasis
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Abstract

This study introduces a novel approach for solving the cosmological field equations within scalar field theory by employing the Eisenhart lift. The field equations are reformulated as a system of geodesic equations for the Eisenhart metric. In the case of an exponential potential, the Eisenhart metric is shown to be conformally flat. By applying basic geometric principles, a new set of dynamical variables is identified, allowing for the linearization of the field equations and the derivation of classical cosmological solutions. However, the quantization of the Eisenhart system reveals a distinct set of solutions for the wavefunction, particularly in the presence of symmetry breaking at the quantum level.

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Andronikos Paliathanasis. 2024-01-11. Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization. https://arxiv.org/abs/2401.05775

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