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

TL;DR

This paper compares the standard inflationary model and a collapse scheme approach in explaining primordial cosmic fluctuations, highlighting differences in their assumptions, fine-tuning issues, and implications for the amplitude of fluctuations.

Contribution

It provides a detailed comparison between the standard inflationary account and a collapse scheme, revealing the latter's potential to avoid fine-tuning but introducing teleological elements.

Findings

Collapse scheme can bypass fine-tuning of the inflaton potential.

Standard account requires inverse proportionality to slow roll parameter.

Collapse approach involves teleological fine-tuning of collapse characteristics.

Abstract

The inflationary paradigm enjoys a very wide acceptance in the cosmological community, due in large part to the fact that it is said to "naturally account" for a nearly scale independent power primordial spectrum of fluctuations which is in very good agreement with the observations. The expected overall scale of the fluctuations in most models, turns out to be too large, because it is inversely proportional to the slow roll parameter, which is expected to be very small. This fact requires the fine tuning of the inflaton potential. In series of recent works it has been argued that the success of the inflationary picture is not fully justified in terms of the rules of quantum theory as applied to the cosmological setting and that an extra element, something akin to a self induced collapse of the wave function is required. There, it was suggested that the incorporation of such collapse in the treatment might avoid the need for fine tuning of the potential that afflicts most inflationary models. In this article we will discuss in detail the manner in which one obtains the estimation of the magnitude of the perturbations in the new scheme and that of the standard accounts, comparing one of the most popular among the later and that corresponding to the new proposal. We will see that the proposal includes a collapse scheme that bypasses the problem, but we will see that the price seems to a be a teleological, and thus unphysical, fine tuning of the characteristics of collapse.