Relativistic minisuperspaces in Finslerian background

Abstract

In one of the approaches to quantization of gravity, the Wheeler–DeWitt equation for the wave function of the universe appeared long ago. Presently, the universe is considered as a micro-universe, a very tiny universe compared to the bigger outer universe to which it belongs. In this work, we will investigate quantum minisuperspaces within the framework of Finslerian spacetime that corresponds to spatially flat FRW background spacetime of the universe. Here, it is possible to convert the Wheeler–DeWitt equation for the wave function of this quantum minisuperspaces into the relativistic quantum mechanical equations, such as Dirac equation, Klein–Gordon equation etc., for the wave function of relativistic subatomic particles. The length scale indicating the smallness of the micro-universe appears in the quantum mechanical equation as the inverse of mass of the subatomic particle. Thus, the relativistic subatomic particles are shown here to be the quantum micro-universe within the bigger universe, such as the one we live in.