  Motivated by recent numerical simulations of molecular cloud (MC)evolution,
in which the clouds engage in global gravitational contraction, and local
collapse events culminate significantly earlier than the global collapse, we
investigate the growth of density perturbations embedded in a collapsing
background, to which we refer as an Inverse Hubble Flow (IHF). We use the
standard procedure for the growth of perturbations in a universe that first
expands (the usual Hubble Flow) and then recollapses (the IHF). We find that
linear density perturbations immersed in an IHF grow faster than perturbations
evolving in a static background (the standard Jeans analysis). A fundamental
distinction between the two regimes is that, in the Jeans case, the time
$\tau_\mathrm{nl}$ for a density fluctuation to become nonlinear increases
without limit as its initial value approaches zero, while in the IHF case
$\tau_\mathrm{nl} \le \tau_\mathrm{ff}$ always, where $\tau_\mathrm{ff}$ is the
free-fall time of the background density. We suggest that this effect, although
moderate, implies that small-scale density fluctuations embedded in
globally-collapsing clouds must collapse earlier than their parent cloud,
regardless of whether the initial amplitude of the fluctuations is moderate or
strongly nonlinear, thus allowing the classical mechanism of Hoyle
fragmentation to operate in multi-Jeans-mass MCs. More fundamentally, our
results show that, contrary to the standard paradigm that fluctuations of all
scales grow at the same rate in the linear regime, the hierarchical nesting of
the fluctuations of different scales does affect their growth even in the
linear stage.
