  We extend various recent results regarding the derivation of effective
cosmological Friedmann equations from the dynamics of group field theory (GFT).
Restricting ourselves to a single GFT field mode (or fixed values of Peter-Weyl
representation labels), we first consider dynamics given by a quadratic
Hamiltonian, which takes the form of a squeezing operator, and then add a
quartic interaction that can be seen as a toy model for interactions in full
GFT. Our derivation of effective Friedmann equations does not require a
mean-field approximation; we mostly follow a general approach in which these
equations in fact hold for any state. The resulting cosmological equations
exhibit corrections to classical Friedmann dynamics similar to those of loop
quantum cosmology, leading to generic singularity resolution, but also involve
further state-dependent terms. We then specify these equations to various types
of coherent states, such as Fock coherent states or Perelomov-Gilmore states
based on the su(1,1) structure of harmonic quantum cosmology. We compute
relative uncertainties of volume and energy in these states, clarifying whether
they can be interpreted as semiclassical. In the interacting case, both
analytical and numerical approximations are used to obtain modified
cosmological dynamics. Our results clarify how effective cosmological equations
derived from GFT can provide reliable approximations to the full dynamics.
