Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity

We reexamine a set of existing procedures aimed at recovering the effective description of the dynamics of loop quantum gravity in the context of cosmological solutions. In particular, the studies of those methods, to which the choice of cuboidal graphs and graph-preserving Hamiltonian is central, result in the formulation of a set of no-go statements, severely limiting the possibility of recovering a physically consistent effective dynamics this way.