  We investigate the parametric amplification of the zero-point fluctuations in
the spin modes of a two-component Bose-Einstein condensate, triggered by the
dynamical evolution of the condensate density. We first make use of a
Thomas-Fermi approximation to develop a tractable theoretical model of the
quantum dynamics of the Bogoliubov excitations in a harmonically trapped
condensate with a time-dependent trapping frequency. The predictions of this
model are then compared to an ab-initio numerical study of the correlation
functions of density and spin fluctuations for general spatially inhomogeneous
configurations. Results are shown for the two cases of expanding and
oscillating condensates: while the quantum excitation of spin modes remains
weak and relatively featureless in the case of an expanding condensate, clear
and experimentally promising signatures of particle creation are anticipated
for the oscillating case under suitable resonance conditions between the
density and the spin modes.
