Effective Theories of Quantum Cosmology

TL;DR

This paper develops and applies effective constraint methods to quantum cosmology models, demonstrating that quantum effects replace the classical Big Bang singularity with a quantum bounce.

Contribution

It introduces two approaches for defining effective constraints and applies them to WDW and Loop Quantum Cosmology models, analyzing their quantum dynamics.

Findings

Quantum bounce replaces Big Bang singularity in Loop Quantum Cosmology.

Effective Hamiltonian constraints are derived up to third order.

Results are consistent with coherent state analysis.

Abstract

We introduce two possible ways of defining effective constraints of quantum systems and applied this effective constraint method to models of WDW Quantum Cosmology and Loop Quantum Cosmology. We analyze effective Hamiltonian constraint on both second and third order and calculate Hubble parameter as well as modified Friedmann equation of each model. Then we compare with a special case using coherent state. It shows that this method is reasonable and as before the classical Big Bang singularity is replaced by a quantum bounce in Loop Quantum Cosmology.