Classical Cancellation of the Cosmological Constant Re-Considered
  We revisit a scenario in which the cosmological constant is cancelled by the potential energy of a slowly evolving scalar field, or "cosmon". The cosmon's evolution is tied to the cosmological constant by a feedback mechanism. This feedback is achieved by an unconventional coupling of the cosmon field to the Ricci curvature scalar. The solutions show that the effective cosmological constant evolves approximately as $t^{-2}$ and remains always of the same order as the density of ordinary matter and radiation. Newton's constant varies on cosmological time scales, with $\dot{G}_N/G_N \ll 1/t$. $G_N$ could have been somewhat different, and possibly smaller, at the time of Big Bang nucleosynthesis. 
Stephen M. Barr, Siew-Phang Ng and Robert J. Scherrer