Constraints on Dark Energy Potentials for Models with Neutrinos Coupled to Dark Energy

A connection is sought between dark energy and the origin of neutrino mass by considering the model of a quintessence scalar field Yukawa-coupled to a massless Dirac fermion field. This model is treated in the framework of finite temperature field theory to generate fermion mass that evolves with the dynamics of the quintessence field. The equation of state obtained in this framework is shown to be consistent with the cosmological evolution of the universe only in the context of specific quintessence potentials. Stricter constraints are found on the free parameters for the corresponding quintessence candidates for which this framework predicts a metastable phase, in accordance with the matter domination epoch, that slowly evolves towards a phase transition at a critical temperature at which the fermion and the scalar masses jump discontinuously to the doomsday vacuum state values. This framework is free from coincidence in scale and fine-tuning problem since the scale of the theory is determined by a single mass parameter of the quintessence potential.