Growth and dissolution of spherical density enhancements in SCDEW
  cosmologies
  Strongly Coupled Dark Energy plus Warm dark matter (SCDEW) cosmologies are
based on the finding of a conformally invariant (CI) attractor solution during
the early radiative expansion, requiring then the stationary presence of $\sim
1\, \%$ of coupled-DM and DE, since inflationary reheating. In these models,
coupled-DM fluctuations, even in the early radiative expansion, grow up to
non-linearity, as shown in a previous associated paper. Such early non-linear
stages are modelized here through the evolution of a top-hat density
enhancement. As expected, its radius $R$ increases up to a maximum and then
starts to decrease. Virial balance is reached when the coupled-DM density
contrast is just 25-26 and DM density enhancement is $\cal O$$(10\, \%)$ of
total density. Moreover, we find that this is not an equilibrium configuration
as, afterwards, coupling causes DM particle velocities to increase, so that the
fluctuation gradually dissolves. We estimate the duration of the whole process,
from horizon crossing to dissolution, and find $z_{horizon}/z_{erasing} \sim 3
\times 10^4$. Therefore, only fluctuations entering the horizon at $z \lesssim
10^9$-$10^{10}$ are able to accrete WDM with mass $\sim 100\, $eV -as soon as
it becomes non-relativistic- so avoiding full disruption. Accordingly, SCDEW
cosmologies, whose WDM has mass $\sim 100\, $eV, can preserve primeval
fluctuations down to stellar mass scale.
