  Nucleation of branes by a four-form field has recently been considered in
string motivated scenarios for the neutralization of the cosmological constant.
An interesting question in this context is whether the nucleation of stacks of
coincident branes is possible, and if so, at what rate does it proceed. Feng et
al. have suggested that, at high ambient de Sitter temperature, the rate may be
strongly enhanced, due to large degeneracy factors associated with the number
of light species living on the worldsheet. This might facilitate the quick
relaxation from a large effective cosmological constant down to the observed
value. Here, we analyse this possibility in some detail. In four dimensions,
and after the moduli are stabilized, branes interact via repulsive long range
forces. Because of that, the Coleman-de Luccia (CdL) instanton for coincident
brane nucleation may not exist, unless there is some short range interaction
which keeps the branes together. If the CdL instanton exists, we find that the
degeneracy factor depends only mildly on the ambient de Sitter temperature, and
does not switch off even in the case of tunneling from flat space. This would
result in catastrophic decay of the present vacuum. If, on the contrary, the
CdL instanton does not exist, coindident brane nucleation may still proceed
through a "static" instanton, representing pair creation of critical bubbles --
a process somewhat analogous to thermal activation in flat space. In that case,
the branes may stick together due to thermal symmetry restoration, and the pair
creation rate depends exponentially on the ambient de Sitter temperature,
switching off sharply as the temperature approaches zero. Such static instanton
may be well suited for the "saltatory" relaxation scenario proposed by Feng et
al.
