Dynamics of Biased Domain Walls and the Devaluation Mechanism
  We study the evolution of biased domain walls in the early universe. We explicitly discuss the roles played by the surface tension and volume pressure in the evolution of the walls, and quantify their effects by looking at the collapse of spherical wall solutions. We then apply our results to a particular mechanism, known as the devaluation scenario, in which the dynamics of biased domain walls was suggested as a possible solution to the cosmological constant problem. Our results indicate that devaluation will in general lead to values of the cosmological constant that differ by several orders of magnitude from the observationally inferred value, $\rho^{1/4}_{vac}\sim10^{-3} \rm eV$. We also argue that the reasons behind this are not specific to a particular realization, and are expected to persist in any scenario of this kind, except if a low energy cut-off on the spectra of vacuum energy densities, of the order of the critical density at the present time, is postulated. This implies that any such scenario will require a fine-tuning similar to the usual one. 
P. P. Avelino, C.J.A.P. Martins, L. Sousa