*Article* **Equivalence of Models in Loop Quantum Cosmology and Group Field Theory**

### **Bekir Bayta¸s, Martin Bojowald \* and Sean Crowe**

Institute for Gravitation and the Cosmos, The Pennsylvania State University, 104 Davey Lab, University Park, PA 16802, USA; bub188@psu.edu (B.B.); stc151@psu.edu (S.C.)

**\*** Correspondence: bojowald@gravity.psu.edu

Received: 29 November 2018; Accepted: 18 January 2019; Published: 23 January 2019

**Abstract:** The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.

**Keywords:** loop quantum cosmology; group field theory; bosonic realizations
