Classical and quantum cosmology of Born-Infeld type models

TL;DR

This paper explores classical and quantum cosmological models involving Born-Infeld type fields, analyzing singularities, quantization methods, and solutions, including difference equations related to black hole quantization.

Contribution

It extends classical solutions and introduces a difference equation approach to Wheeler-DeWitt quantization for Born-Infeld cosmological models.

Findings

Classical solutions exhibit singularities.

Quantization yields explicit solutions for constant potential.

Difference equations reveal unique solution features.

Abstract

We discuss Born-Infeld type fields (tachyon fields) in classical and quantum cosmology. We first partly review and partly extend the discussion of the classical solutions and focus in particular on the occurrence of singularities. For quantization, we employ geometrodynamics. In the case of constant potential, we discuss both Wheeler-DeWitt quantization and reduced quantization. We are able to give various solutions and discuss their asymptotics. For the case of general potential, we transform the Wheeler-DeWitt equation to a form where it leads to a difference equation. Such a difference equation was previously found in the quantization of black holes. We give explicit results for the cases of constant potential and inverse squared potential and point out special features possessed by solutions of the difference equation.