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We study a new field theory effect in the cosmological context in the TwoMeasures Field Theory (TMT). TMT is an alternative gravity and matter fieldtheory where the gravitational interaction of fermionic matter is reduced tothat of General Relativity when the energy density of the fermion matter ismuch larger than the dark energy density. In this case also the 5-th forceproblem is solved automatically. In the opposite limit, where the magnitudes offermionic energy density and scalar field dark energy density becomecomparable, nonrelativistic fermions can participate in the cosmologicalexpansion in a very unusual manner. Some of the features of such states in atoy model of the late time universe filled with homogeneous scalar field anduniformly distributed nonrelativistic neutrinos: neutrino mass increases as m ~a^{3/2}; the neutrino gas equation-of-state approaches w=-1, i.e. neutrinosbehave as a sort of dark energy; the total (scalar field + neutrino)equation-of-state also approaches w=-1; the total energy density of suchuniverse is less than it would be in the universe filled with the scalar fieldalone. An analytic solution is presented. A domain structure of the dark energyseems to be possible. We speculate that decays of the CLEP state neutrinos maybe both an origin of cosmic rays and responsible for a late super-accelerationof the universe. In this sense the CLEP states exhibit simultaneously newphysics at very low densities and for very high particle masses.Comment: 47 pages, accepted for publication in Int.J.Mod.Phys.

EXOTIC LOW DENSITY FERMION STATES IN THE TWO MEASURES FIELD THEORY: NEUTRINO DARK ENERGY