The collapse of the wave function in the joint metric-matter   quantization for inflation
  It has been argued that the standard inflationary scenario suffers from a serious deficiency as a model for the origin of the seeds of cosmic structure: it can not truly account for the transition from an early homogeneous and isotropic stage to another one lacking such symmetries. The issue has often been thought as a standard instance of the "quantum measurement problem", but as has been recently argued by some of us the situation reaches a critical level in the cosmological context of interest here. This has lead to a proposal in which the standard paradigm is supplemented by a hypothesis concerning the self-induced dynamical collapse of the wave function, as representing the physical mechanism through which such change of symmetry is brought forth. This proposal was formulated within the context of semiclassical gravity. Here we investigate an alternative realization of such idea implemented directly within the standard analysis in terms of a quantum field jointly describing the inflaton and metric perturbations, the so called Mukhanov-Sasaki variable. We show that even though the prescription is quite different, the theoretical predictions include some deviations from the standard ones, which are indeed very similar to those found in the early studies. We briefly discuss the differences between the two at both, the conceptual and practical levels. 
Alberto Diez-Tejedor, Gabriel Le\'on and Daniel Sudarsky
gr-qc