# The Finslerian quantum cosmology

## TL;DR

This paper develops a quantum cosmological model based on Finslerian geometry, deriving solutions to the Wheeler-DeWitt and Schrödinger equations, and analyzing the universe's scale factor evolution.

## Contribution

It introduces a Finslerian geometric framework into quantum cosmology and provides exact classical and quantum solutions for the universe's wave function.

## Key findings

- Exact solutions for the wave function of the universe.
- Analysis of the expectation value of the scale factor over time.
- Discussion of the physical implications of Finslerian quantum cosmology.

## Abstract

We present a Friedmann-Robertson-Walker (FRW) quantum cosmological model within the framework of Finslerian geometry. In this work, we consider a specific fluid. We obtain the corresponding Wheeler-DeWitt equation as the usual constraint equation as well as Schr\"odinger equation following Dirac, although the approaches yields the same equation of time independent equation for the wave function of the universe. We provide exact classical and quantum mechanical solutions. We use the eigenfunctions to study the time evolution of the expectation value of the scale factor. Finally we discuss the physical meaning of the results.