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 yet unknown fundamental theory, at energy scale below M_{p} has the form of expansion in two measures: S=\intd^{4}x[\Phi L_{1}+\sqrt{-g}L_{2}] where the new measure \Phi is defined using the third-rank antisymmetric tensor. In the new variables (Einstein frame) all equations of motion take canonical GR form and therefore models are free of the well-known "defects" that distinguish the Brans-Dicke type theories from GR. All novelty is revealed only in an unusual structure of the effective potential U(\phi) and interactions which turns over intuitive ideas based on our experience in field theory. E.g. the greater \Lambda we admit in L_{2}, the smaller U(\phi) will be in the Einstein picture. Field theory models are suggested with explicitly broken global continuos symmetry which in the Einstein frame has the form \phi\to\phi+const. The symmetry restoration occurs as \phi\to\infty. A few models are presented where U is produced with the following shape: for \phi<-M_{p}, U has the form typical for inflation model, e. g. U=\lambda\phi^4 with \lambda\sim 10^{-14}; for\phi>-M_{p}, U has mainly exponential form U\sim e^{-a\phi/M_{p}} with variable a: a=14 for -M_{p}<\phi<M_{p} that admits nucleosynthesis; a=2 for \phi>M_{p} that implies quintessence era. There is no need in any fine tuning to prevent appearance of the CC term or any other terms that could violate flatness of U at \phi\ggM_{p}. \lambda\sim 10^{-14} is obtained without fine tuning as well. Quantized matter fields models, including gauge theories with SSB can be incorporated without altering mentioned above results. Direct fermion-inflaton coupling resembles Wetterich's model but it does not lead to any observable effect at present. SSB does not raise any problem with CC. 
A.B. Kaganovich