Viability of slow-roll inflation in light of the non-zero k_min measured in the CMB power spectrum

TL;DR

This paper examines whether slow-roll inflation models can accommodate a non-zero minimum wavenumber in the CMB spectrum, finding that most models fail unless they violate slow-roll conditions, thus challenging the conventional inflationary paradigm.

Contribution

It provides a quantitative analysis showing that a non-zero k_min conflicts with standard slow-roll inflation, especially when considering extensions like kinetic or radiation-dominated phases.

Findings

Most slow-roll models cannot fit the k_min > 0 data without violating slow-roll conditions.

Models with epsilon > 0.9 predict spectral indices inconsistent with observations.

Extensions to the model do not resolve the horizon problem alongside the k_min issue.

Abstract

Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum P(k). These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest Planck release suggests that P(k) has a hard cutoff, k_min > 0, inconsistent with this conventional picture. Here we demonstrate quantitatively that most---perhaps all---slow-roll inflationary models fail to accommodate this minimum cutoff. We show that the small parameter `epsilon' must be > 0.9 throughout the inflationary period to comply with the data, seriously violating the slow-roll approximation. Models with such an epsilon predict extremely red spectral indices, at odds with the measured value. We also consider extensions to the basic picture (suggested by several earlier workers) by adding a kinetic-dominated or radiation-dominated phase preceding the slow-roll expansion. Our approach differs from previously published treatments principally because we require these modifications to---not only fit the measured fluctuation spectrum, but to simultaneously also---fix the horizon problem. We show, however, that even such measures preclude a joint resolution of the horizon problem and the missing correlations at large angles.