Viability of slow-roll inflation in light of the non-zero kmin measured in the cosmic microwave background power spectrum

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 cut off, k(min) not equal 0, inconsistent with this conventional picture. Here, we demonstrate quantitatively that most-perhaps all-slow-roll inflationary models fail to accommodate this minimum cut-oft. We show that the small parameter epsilon must be greater than or similar to 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 not only to fit the measured fluctuation spectrum but also simultaneously to 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.