  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.
