Generalized Gaussian states in group field theory and su(1,1) quantum cosmology

We define generalized Gaussian states for quantum cosmological models based on the su(1,1) algebra, with particular emphasis on its realization in group field theory for a single field mode, and study their semiclassical properties. These states are generalizations of coherent, squeezed, and thermal states considered previously. As two possible characterizations of semiclassicality, we contrast the requirement of small relative fluctuations in volume and energy with the saturation of the Robertson-Schr\"odinger uncertainty principle. We find that for the most general class of states, the appearance of small relative fluctuations, which we take as the main criterion relevant for the emergence of cosmology, is mostly determined by the amount of displacement used to define the state. We also observe that defining such generalized Gaussian states is less straightforward in the algebraic approach to canonical quantization of group field theory, and discuss special cases.