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Summary of abstract Field theory models including gauge theories with SSB arepresented where the energy density of the true vacuum state (TVS) is zerowithout fine tuning. The above models are constructed in the gravitationaltheory where a measure of integration \Phi in the action is not necessarily\sqrt{-g} but it is determined dynamically through additional degrees offreedom. The ratio \Phi/\sqrt{-g} is a scalar field which can be solved interms of the matter degrees of freedom due to the existence of a constraint. Westudy a few explicit field theory models where it is possible to combine thesolution of the cosmological constant problem with: 1) possibility forinflationary scenario for the early universe; 2) spontaneously broken gaugeunified theories (including fermions). The models are free from the well knownproblem of the usual scalar-tensor theories in what is concerned with theclassical GR tests. The only difference of the field equations in the Einsteinframe from the canonical equations of the selfconsistent system of Einstein'sgravity and matter fields, is the appearance of the effective scalar fieldpotential which vanishes in TVS without fine tuning.Comment: Extended version of the contribution to the fourth Alexander  Friedmann International Seminar on Gravitation and Cosmology; accepted for  publication in Phys. Rev. D; 31 page

Dynamical measure and field theory models free of the cosmological constant problem