Dynamical measure and field theory models free of 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 be not necessarily -g but be determined dynamically through additional degrees of freedom, like four scalar fields ₀. We study three possibilities for the general structure of the theory. (A) The total action has the form S=d^4x where the measure is built from the scalars ₀ in such a way that the transformation LL+const does not affect the equations of motion. Then an infinite dimensional shift group of the measure fields (SGMF) ₀ by arbitrary functions of the Lagrangian density L, ₀₀+f₀ (L), is recognized as the symmetry group of the action up to an integral of total divergence. (B) The total action has the form S=S₁+S₂, S₁=L₁d^4x, S₂=-gL₂d^4x which is the only model different from (A) and invariant under the SGMF but now with f₀=f₀ (L₁). Similarly, now only S₁ satisfies the requirement that the transformation L₁L₁+const not affect the equations of motion. In both cases (A) and (B) it is assumed that L, L₁, L₂ do not depend on ₀. (C) The action includes a term which breaks the SGMF symmetry. It is shown that in the first order formalism a constraint appears which allows us to solve the scalar field related to the dynamical measure degrees of freedom in terms of matter fields. The remarkable feature of the models discussed in this paper is that for all cases (A), (B), and (C), after the change of variables to the conformal Einstein frame, the classical field equations take exactly the form of general relativity (GR). Therefore the models are free from the well-known problem of the usual scalar-tensor theories in what concerns the classical GR tests. The only difference of the field equations in the Einstein frame from the canonical equations of the self-consistent system of Einstein's gravity and matter fields is the appearance of the effective scalar field potential which vanishes in a true vacuum state (TVS) without fine-tuning in cases (A) and (B). To illustrate how the theory works, we present a few explicit field theory models where it is possible to combine the solution of the CCP with (1) the possibility for an inflationary scenario, and (2) spontaneously broken gauge unified theories (including fermions). In 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 in S₁, the continuous symmetry +const is respected. Surprisingly, in this case spontaneous symmetry breaking takes place while no massless (``Goldstone'') boson appears. We discuss the role of the SGMF symmetry for quantization and the possible connection of this theory with theories of extended objects.