  The standard inflationary account for the origin of cosmic structure is,
without a doubt, extremely successful. However, it is not fully satisfactory as
has been argued in [A. Perez, H. Sahlmann, and D. Sudarsky, Class. Quantum
Grav., 23, 2317, (2006), arXiv:gr-qc/0508100]. The central point is that, in
the standard accounts, the inhomogeneity and anisotropy of our universe seems
to emerge, unexplained, from an exactly homogeneous and isotropic initial state
through processes that do not break those symmetries. The proposal made there
to address this shortcoming calls for a dynamical and self-induced quantum
collapse of the original homogeneous and isotropic state of the inflaton. In
this article, we consider the possibility of a multiplicity of collapses in
each one of the modes of the Quantum Field. As we will see, the results are
sensitive to a more detailed characterization of the collapse than those
studied in the previous works, and in this regard two simple options will be
studied. We find important constraints on the model, most remarkably on the
number of possible collapses for each mode.
