Hamiltonian group field theory with multiple scalar matter fields

One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field theory leading to a Hamiltonian formulation in which states or operators evolve with respect to the clock given by a free massless scalar field, similar to what happens in deparametrised models in quantum cosmology. Here we extend the construction of Hamiltonian group field theory to models with multiple scalar matter fields, encountering new features and technical subtleties compared with the previously studied case. We show that the effective cosmological dynamics for these more general models reduce to the Friedmann dynamics of general relativity with multiple scalar fields in the limit of large volume, if suitable (non-generic) initial conditions are chosen. At high energy, we find corrections to the classical Friedmann equations whose form is similar to what is found in loop quantum cosmology. These corrections lead to generic singularity resolution by a bounce. For generic initial conditions, the effective cosmological dynamics treat the 'clock' field and other matter fields differently, in disagreement with the Friedmann dynamics of general relativity. We speculate on a possible interpretation in terms of inhomogeneities.