FRW barotropic zero modes: Dynamical systems observability
  The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmological oscillators are investigated. Nonlinear techniques for dynamical analysis have been recently developed in many engineering areas but their application has not been extended beyond their standard field. This paper is a small contribution to an extension of this type of dynamical systems analysis to FRW barotropic cosmologies. We find that determining the Hubble parameter of barotropic FRW universes does not allow the observability, i.e., the determination of neither the barotropic FRW zero mode nor of its derivative as dynamical cosmological states. Only knowing the latter ones correspond to a rigorous dynamical observability in barotropic cosmology 
H.C. Rosu, V. Ibarra-Junquera