Dynamical mechanism of vacuum energy compensation

The model of vacuum energy compensation due to interaction of a scalar field $\phi$ with curvature scalar of the form $\beta R \phi^2 f(\phi)$ is proposed. It is shown that with a simple power form of $f(\phi)$ the exponential expansion, induced by vacuum energy (or what is the same by cosmological constant), is transformed into canonical cosmological evolution of the universe dominated by relativistic matter.