Stepping out of Homogeneity in Loop Quantum Cosmology

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.

16 pages

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Cited by in corpus (10)

• Towards Spinfoam Cosmology
• Consistent Loop Quantum Cosmology
• Cosmological constant in spinfoam cosmology
• A new look at loop quantum gravity
• Dynamics for a 2-vertex Quantum Gravity Model
• Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model
• Local spinfoam expansion in loop quantum cosmology
• Vertex Expansion for the Bianchi I model
• Coherent states for FLRW space-times in loop quantum gravity
• Big Bounce in Dipole Cosmology