The role of cosmological constant in f(R, G) gravity

Einstein-Hilbert action is supplemented by the Gauss-Bonnet squared term, its phase-space structure is constructed and canonical quantization is performed. Resolution of a contradiction that emerges in the process, requires the presence of other fields at least in the form of vacuum energy-density, commonly known as the cosmological constant. This reveals the very importance of the presence of other fields at least in the form of the cosmological constant, in the very early universe.