Generalized quantum gravity condensates for homogeneous geometries and cosmology

TL;DR

This paper develops a new class of quantum gravity condensate states that describe homogeneous geometries, improving previous models by incorporating topology and enabling applications to cosmology and spherical symmetry.

Contribution

It introduces a generalized condensate construction using infinite superpositions and refinement operators, enhancing the modeling of continuum homogeneous quantum geometries in loop quantum gravity.

Findings

Constructed a new class of quantum gravity condensates for homogeneous geometries.

Demonstrated the applicability to spherically symmetric quantum geometries.

Provided a framework for connecting quantum states to continuum cosmological models.

Abstract

We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction lends itself easily to be applied also to the case of spherically symmetric quantum geometries.