Field Theory Models without the Cosmological Constant Problem

We study field theory models in the context of a gravitational theory without the cosmological constant problem (CCP). The theory is based on the requirement that the measure of integration in the action is not necessarily √− g but it is determined dynamically through additional degrees of freedom, like four scalar fields ϕ a . We study three possibilities for the general structure of the theory: (A) The total action has the form S = R Φ Ld 4 x where the measure Φ is built from the scalars ϕ a in such a way that the transformation L → L + const does not effect equations of motion. Then an infinite dimensional shifts group of the measure fields (SGMF) ϕ a by arbitrary functions of the Lagrangian density L ϕ a → ϕ a + f a ( L ) is recognized as the symmetry group of the action up to an integral of a total divergence. The total action has the form which is the only model different from (A) and invariant under SGMF (but now with f a = f a ( L 1 )). Similarly, now only S 1 satisfies the requirement that the transformation L 1 → L 1 + const does not effect equations of motion. Both in the case (A) and in the case (B) it is assumed that L, L 1 , L 2 do not depend on ϕ a . (C) The action includes a term which breaks the SGMF symmetry. It is shown that in the first order formalism in cases (A) and (B) the CCP is solved: the effective potential vanishes in a true vacuum state (TVS) without fine tuning. We present a few explicit field theory models where it is possible to combine the solution of the CCP with: 1) possibility for inflationary scenario; 2) spontaneously broken gauge unified theories (including fermions). In the case (C), the breaking of the SGMF symmetry induces a nonzero energy density for the TVS. When considering only a linear potential for a scalar field φ in S 1 , the continuous symmetry φ → φ + const is respected. Surprisingly, in this case SSB takes place while no massless (”Gold-stone”) boson appears. We discuss the role of the SGMF symmetry in the possible connection of this theory with theories of extended objects.