  We study the spectrum of cosmological fluctuations in the D3/D7 brane
inflationary universe with particular attention to the parametric excitation of
entropy modes during the reheating stage. The same tachyonic instability which
renders reheating in this model very rapid leads to an exponential growth of
entropy fluctuations during the preheating stage which in turn may induce a
large contribution to the large-scale curvature fluctuations. We take into
account the effects of long wavelength quantum fluctuations in the matter
fields. As part of this work, we perform an analytical analysis of the
reheating process. We find that the initial stage of preheating proceeds by the
tachyonic instability channel. An upper bound on the time it takes for the
energy initially stored in the inflaton field to convert into fluctuations is
obtained by neglecting the local fluctuations produced during the period of
tachyonic decay and analyzing the decay of the residual homogeneous field
oscillations, which proceeds by parametric resonance. We show that in spite of
the fact that the resonance is of narrow-band type, it is sufficiently
efficient to rapidly convert most of the energy of the background fields into
matter fluctuations.
