Perturbing a quantum gravity condensate

TL;DR

This paper explores the initial steps in understanding cosmological perturbations within a quantum gravity condensate framework, deriving classical perturbation procedures from fundamental quantum gravity principles.

Contribution

It introduces a method to study homogeneous metric perturbations in a quantum gravity condensate model, linking quantum gravity dynamics to quantum cosmology.

Findings

Perturbations are modeled as single atoms added to a homogeneous condensate.

Backreaction of perturbations on the background is negligible.

Derivation of classical quantum cosmology procedures from quantum gravity.

Abstract

In a recent proposal using the group field theory approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of "atoms of space," which allows the derivation of an effective cosmological Friedmann equation from the microscopic quantum gravity dynamics. Here we take a first step towards the study of cosmological perturbations over the homogeneous background. We consider a state in which a single "atom" is added to an otherwise homogeneous condensate. Backreaction of the perturbation on the background is negligible and the background dynamics can be solved separately. The dynamics for the perturbation takes the form of a quantum cosmology Hamiltonian for a "wave function," depending on background and perturbations, of the product form usually assumed in a Born-Oppenheimer approximation. We show that the perturbation we consider corresponds to a spatially homogeneous metric perturbation, and for this case derive the usual procedures in quantum cosmology from fundamental quantum gravity.