Classical and quantum cosmology of Born-Infeld type models

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.

14 pages, 8 figures, published version

References in corpus (5)

• Quantum phantom cosmology
• Quantum cosmology with big-brake singularity
• On the quantum fate of singularities in a dark-energy dominated universe
• Will the tachyonic Universe survive the Big Brake?
• Late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state

Cited by in corpus (10)

• Singularity avoidance in Bianchi I quantum cosmology
• Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities
• Phantom singularities and their quantum fate: general relativity and beyond
• Towards the Quantization of Eddington-inspired-Born-Infeld Theory
• Classical and quantum cosmology of the little rip abrupt event
• On the dynamics of the general Bianchi IX spacetime near the singularity
• Future soft singularities, Born-Infeld-like fields and particles
• Nonlinear Problems Inspired by the Born--Infeld Theory of Electrodynamics
• Analyzing quantum gravity spillover in the semiclassical regime
• Again About Singularity Crossing In Gravitation And Cosmology