Towards Spinfoam Cosmology

TL;DR

This work formulates a covariant spinfoam cosmology by projecting loop quantum gravity onto a cosmological sector using holomorphic coherent states and a dipole graph. At first order in the vertex expansion and in a large-volume limit, the authors derive a transition amplitude between homogeneous-isotropic states that lies in the kernel of a quantum constraint whose classical limit reproduces the Friedmann Hamiltonian for flat FRW cosmology, indicating a recovery of Friedmann dynamics from full LQG in this regime. The analysis clarifies how cosmological dynamics emerge from a background-independent quantum gravity framework and discusses limitations due to Euclidean signature and absence of matter, while outlining clear paths to extend the framework to larger graphs, higher-order corrections, and inclusion of inhomogeneous fluctuations. Overall, the paper provides a concrete, calculable bridge between covariant LQG and classical cosmology, offering a controlled avenue to study quantum gravitational effects in the early universe and at the bounce. The approach complements loop quantum cosmology by starting from the full theory and applying a cosmological truncation and expansion, with potential applications to inhomogeneous fluctuations and quantum gravity phenomenology.

Abstract

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.