  Summary of abstract Field theory models including gauge theories with SSB are
presented where the energy density of the true vacuum state (TVS) is zero
without fine tuning. The above models are constructed in the gravitational
theory where a measure of integration \Phi in the action is not necessarily
\sqrt{-g} but it is determined dynamically through additional degrees of
freedom. The ratio \Phi/\sqrt{-g} is a scalar field which can be solved in
terms of the matter degrees of freedom due to the existence of a constraint. We
study a few explicit field theory models where it is possible to combine the
solution of the cosmological constant problem with: 1) possibility for
inflationary scenario for the early universe; 2) spontaneously broken gauge
unified theories (including fermions). The models are free from the well known
problem of the usual scalar-tensor theories in what is concerned with the
classical GR tests. The only difference of the field equations in the Einstein
frame from the canonical equations of the selfconsistent system of Einstein's
gravity and matter fields, is the appearance of the effective scalar field
potential which vanishes in TVS without fine tuning.
