  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.
