Cosmological model with dynamical cancellation of vacuum energy and dark energy

We propose a model with a compensating scalar field whose back reaction to the cosmological curvature cancels possible vacuum energy density down to the terms of the order of the time-dependent critical energy density. Thus, the model simultaneously solves the mystery of the compensation of vacuum energy with an accuracy of 120 orders of magnitude and explains the existence of the observed dark energy. At an early stage, the suggested cosmological model might experience exponential expansion without an additional inflaton field. However, the solution found is unstable with respect to small perturbations. The stability can be ensured by introducing nonanalytical terms depending upon the absolute value of the curvature scalar R. Unfortunately, stable solutions do not describe realistic cosmology at the matter-dominated stage.