Hamiltonian group field theory with multiple scalar matter fields

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