  We propose a simple model that provides a dynamical cancellation mechanism of
the vacuum energy density appearing either in the form of a bare cosmological
constant, quantum fluctuations of matter fields or the result of phase
transitions. This `conformal compensator model' is based on a conformal
coupling $A(\varphi)$ between the Einstein and the Jordan frames. This couples
a second scalar field $\lambda$ to the trace of the matter energy-momentum
tensor, including the bare cosmological constant, and serves as a dynamical
Lagrange multiplier. As a result, the scalar $\lambda$ relaxes to a value which
cancels the contributions from the vacuum energy density to the Friedmann
equation, and adjusts itself to changes of the vacuum energy density after
matter phase transitions. This circumvents Weinberg's theorem through the time
dependence of the background scalar field $\varphi$. The radiation era, where
the vacuum energy is annulled, is recovered in a natural manner. It is also
possible to recover the matter era, via a tracking of the matter energy density
by the scalar field, as well as the inflationary and dark energy eras, which
correspond to regimes where the cancellation mechanism becomes inefficient.
This suggests that inflation, dark energy, and the annulation of the vacuum
energy density, could be related to the same mechanism. In this setting, the
usual fine-tuning of the vacuum energy is avoided, although the onset of the
dark energy era at the appropriate time is not explained.
