Time-dependent toroidal compactification proposals and the Bianchi type II model: classical and quantum solutions

TL;DR

This paper develops a four-dimensional cosmological model from ten-dimensional gravity with a scalar field, analyzing classical and quantum solutions for anisotropic Bianchi type II universes with time-dependent compactification.

Contribution

It introduces a novel approach to compactify extra dimensions without fluxes and explores classical and quantum solutions for Bianchi type II models with moduli fields.

Findings

Derived classical solutions for anisotropic scale factors and moduli fields.

Presented quantum solutions to the Wheeler-DeWitt equation for Bianchi models.

Compared quantum solutions with Bohm's approach, linking to WKB approximation.

Abstract

In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus without the contributions of fluxes as first approximation. This approach is applied to anisotropic cosmological Bianchi type II model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Also, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology and we claim that these quantum solution are generic in the moduli scalar field for all Bianchi Class A models. Also we gives the relation to these solutions for asymptotic behavior to large argument in the corresponding quantum solution in the gravitational variables and is compared with the Bohm's solutions, finding that this corresponds to lowest-order WKB approximation.