Semiclassical self consistent treatment of the emergence of seeds of cosmic structure. The second order construction

In this work we extend the results of [1] where, Semiclassical Selfconsistent Configurations (SSC) formalism was introduced. The scheme combines quantum field theory on a background space-time, semiclassical treatment of gravitation and spontaneous collapse theories. The approach is applied to the context of early universe cosmology using a formal description of the transition from an initial inflationary stage characterized by a spatially homogeneous and isotropic (H&I) universe, to another where inhomogeneities are present in association with quantum fluctuations of the field driving inflation. In that work two constructions are produced. One of them describes a universe that is completely spatially homogeneous and isotropic, and the other is characterized by a slight excitation of the particular inhomogeneous and anisotropic perturbation. Finally, a characterization of their gluing to each other is provided as representing the transition as a result from a spontaneous collapse of the state of the quantum field, following the hypothesis originally introduced in [2]. Specifically, in [1] this construction is carried out by using cosmological perturbation theory and working up to linear order in the perturbation. However, given the nonlinear nature of gravitation, we should in principle explore the application of the formalism in a nonlinear regime. To this end and as a first step, we study in this work the transition from a spatially homogeneous and isotropic (H&I) Semiclassical Self-Consistent Configuration (SSC-I) to one SSC-II that is not spatially (H&I), working this time up to second order in perturbation theory. We find that the self consistent construction now requires consideration of the so called tensor modes, as well as a nontrivial mixing of modes that made the analysis much more difficult and which could not a priori be warranted to work out in detail. The present work shows that this is indeed the case.