Stepping out of Homogeneity in Loop Quantum Cosmology

TL;DR

This paper extends loop quantum cosmology to include inhomogeneous degrees of freedom, connecting it more closely with full loop quantum gravity and exploring effective dynamics near the initial singularity.

Contribution

It introduces a model incorporating inhomogeneities in loop quantum cosmology, demonstrating the reduction to standard cosmology in the Born-Oppenheimer approximation and validating effective dynamics.

Findings

Model with inhomogeneous degrees of freedom near singularity

Reduction to loop quantum cosmology in Born-Oppenheimer approximation

Viable effective dynamics using non-graph-changing Hamiltonian constraint

Abstract

We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable effective dynamics within this approximation.