The Einstein equations for an isotropic and homogeneous Friedmann-Robertson-Walker universe in the presence of a quintessence scalar field are shown to be described in a compact way, formally identical to the dynamics of a relativistic particle moving on a two-dimensional spacetime. The correct Lagrangian for the system is presented and used to construct a spinor quantum cosmology theory using Breit’s prescription. The theory is supersymmetric when written in the Majorana representation. The spinor field components interact through a potential that correlates the spacetime metric and the quintessence. An exact supersymmetric solution for $k=0$ case is exhibited. This quantum cosmology model may be interpreted as a theory of interacting universes.

• Received 9 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.083518