Cosmological Plebanski theory

TL;DR

This paper explores a simplified cosmological model derived from Plebanski theory to investigate quantum gravity issues, analyzing classical solutions and quantization effects, including the role of the Immirzi parameter.

Contribution

It provides a classical and quantum analysis of a cosmological Plebanski model, highlighting the mixing of topological and gravitational solutions and the impact of the Immirzi parameter.

Findings

Quantum mixing of solutions prevents equivalence to standard quantum cosmology.

Topological solutions dominate in the classical limit.

Immirzi parameter influences the model's quantum properties.

Abstract

We consider the cosmological symmetry reduction of the Plebanski action as a toy-model to explore, in this simple framework, some issues related to loop quantum gravity and spin-foam models. We make the classical analysis of the model and perform both path integral and canonical quantizations. As for the full theory, the reduced model admits two types of classical solutions: topological and gravitational ones. The quantization mixes these two solutions, which prevents the model to be equivalent to standard quantum cosmology. Furthermore, the topological solution dominates at the classical limit. We also study the effect of an Immirzi parameter in the model.