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The inflationary paradigm enjoys a very wide acceptance in the cosmologicalcommunity, due in large part to the fact that it is said to "naturally account"for a nearly scale independent power primordial spectrum of fluctuations whichis in very good agreement with the observations. The expected overall scale ofthe fluctuations in most models, turns out to be too large, because it isinversely proportional to the slow roll parameter, which is expected to be verysmall. This fact requires the fine tuning of the inflaton potential. In seriesof recent works it has been argued that the success of the inflationary pictureis not fully justified in terms of the rules of quantum theory as applied tothe cosmological setting and that an extra element, something akin to a selfinduced collapse of the wave function is required. There, it was suggested thatthe incorporation of such collapse in the treatment might avoid the need forfine tuning of the potential that afflicts most inflationary models. In thisarticle we will discuss in detail the manner in which one obtains theestimation of the magnitude of the perturbations in the new scheme and that ofthe standard accounts, comparing one of the most popular among the later andthat corresponding to the new proposal. We will see that the proposal includesa collapse scheme that bypasses the problem, but we will see that the priceseems to a be a teleological, and thus unphysical, fine tuning of thecharacteristics of collapse.

classical and quantum gravity

The slow roll condition and the amplitude of the primordial spectrum of  cosmic fluctuations: Contrasts and similarities of standard account and the  "collapse scheme"