Field theory model giving rise to quintessential inflation without the cosmological constant and other fine-tuning problems

A field theory is developed based on the idea that the effective action of a yet unknown fundamental theory, at an energy scale below the Planck mass M-p, has the form of expansion in two measures: S = integrald(4)x[PhiL(1) + root -gL(2)], where the new measure Phi is defined using the antisymmetric tensor field Phid(4)x=partial derivative ([alpha)A(beta gamma delta])dx(alpha) boolean AND dx(beta)boolean AND dx(gamma)boolean AND dx(delta). A shift L-1-->L-1 + const does not affect the equations of motion, whereas a similar shift when implementing with L-2 causes a change which in standard GR would be equivalent to that of the cosmological constant (CC) term. The next basic conjecture is that the Lagrangian densities L-1 and L-2 do not depend on A(mu nu lambda). The new measure degrees of freedom result in the scalar field chi = Phi/root -g alone. A constraint appears that determines chi in terms of matter fields. After the conformal transformation to the new variables (Einstein frame), all equations of motion take the canonical GR form of the equations for gravity and matter fields and, therefore, the models we study are free of the well-known defects that distinguish the Brans-Dicke type theories from Einstein's GR. All novelty is revealed only in an unusual structure of the effective potentials and interactions which turn over our intuitive ideas based on our experience in field theory. For example, the greater Lambda we admit in L-2, the smaller magnitude of the effective inflaton potential U(phi) will there be in the Einstein picture. Field theory models are suggested with explicitly broken global continuous symmetry, which in the Einstein frame has the form phi-->phi+ const. The symmetry restoration occurs as phi -->infinity. A few models are presented where the effective potential U(phi) is produced with the following shape: for phi less than or similar to -M-p, U(phi) has the form typical for inflation model, e.g., U = lambda phi (4) with lambda similar to 10(-14); for phi greater than or similar to - M-p, U(phi) has mainly the exponential form U similar to e(-a phi /M)p with variable a; a = 14 for -M-p greater than or similar to phi less than or similar to M-p, which gives the possibility for nucleosynthesis and large-scale structure formation; and a = 2 for phi greater than or similar toM(p), which implies the quintessence era. There is no need far any fine-tuning to prevent the appearance of the CC term or any other terms that could violate the flatness of U(phi) at phi>>M-p. lambda similar to 10(-14) is Obtained Without fine-tuning as well. Quantized matter field models, including spontaneously broken gauge theories, can be incorporated without altering the results mentioned above. Direct coupling of fermions to the inflaton resembles Wetterich's model, but there is a possibility to avoid any observable effect at the late universe. SSB does not raise any problems with the CC in the late universe.