  We consider two spatially flat Friedmann-Robertson-Walker spacetimes divided
by a time-like thin shell in the nontrivial case in which the inner region of
finite extension contains radiation and the outer region is filled with dust.
We will then show that, while the evolution is determined by a large set of
constraints, an analytical description for the evolution of the bubble radius
can be obtained by formally expanding for short times after the shell attains
its minimum size. In particular, we will find that a bubble of radiation,
starting out with vanishing expansion speed, can be matched with an expanding
dust exterior, but not with a collapsing dust exterior, regardless of the dust
energy density. The former case can then be used to describe the nucleation of
a bubble of radiation inside an expanding dust cloud, although the final
configuration contains more energy than the initial dust, and the reverse
process, with collapsing radiation transforming into collapsing dust, is
therefore energetically favored. We however speculate a (small) decaying vacuum
energy or cosmological constant inside dust could still trigger nucleation.
Finally, our perturbative (yet analytical) approach can be easily adapted to
different combinations of matter inside and outside the shell, as well as to
more general surface density, of relevance for cosmology and studies of defect
formation during phase transitions.
