Towards a formal description of the collapse approach to the inflationary origin of the seeds of cosmic structure

Inflation plays a central role in our current understanding of the universe. According to the standard viewpoint, the homogeneous and isotropic mode of the inflaton field drove an early phase of nearly exponential expansion of the universe, while the quantum fluctuations (uncertainties) of the other modes gave rise to the seeds of cosmic structure. However, if we accept that the accelerated expansion led the universe into an essentially homogeneous and isotropic space-time, with the state of all the matter fields in their vacuum (except for the zero mode of the inflaton field), we can not escape the conclusion that the state of the universe as a whole would remain always homogeneous and isotropic. It was recently proposed in [A. Perez, H. Sahlmann and D. Sudarsky, "On the quantum origin of the seeds of cosmic structure," Class. Quant. Grav. 23, 2317-2354 (2006)] that a collapse (representing physics beyond the established paradigm, and presumably associated with a quantum-gravity effect a la Penrose) of the state function of the inflaton field might be the missing element, and thus would be responsible for the emergence of the primordial inhomogeneities. Here we will discuss a formalism that relies strongly on quantum field theory on curved space-times, and within which we can implement a detailed description of such a process. The picture that emerges clarifies many aspects of the problem, and is conceptually quite transparent. Nonetheless, we will find that the results lead us to argue that the resulting picture is not fully compatible with a purely geometric description of space-time.