Group field cosmology: a cosmological field theory of quantum geometry

TL;DR

This paper develops a group field theory approach to quantum cosmology, modeling the wavefunction as a field over minisuperspace variables, and explores classical solutions, quantum propagators, and mean-field approximations with various interactions.

Contribution

It introduces a novel minisuperspace model within group field theory, incorporating nonlinear interactions to simulate different cosmological effects.

Findings

Derived classical solutions for the model

Analyzed the quantum propagator in this framework

Showed how different interactions can mimic cosmological constants or matter effects

Abstract

Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.