CMB targets after the latest Planck data release

Abstract

We show that a combination of the simplest $\alpha$-attractors and KKLTI models related to Dp-brane inflation covers most of the area in the ($n_s$, $r$) space favored by Planck 2018. For $\alpha$-attractor models, there are discrete targets $3\alpha =1,2,...,7$, predicting 7 different values of $r=12\alpha /N^2$ in the range $10^{-2}\gtrsim r\gtrsim 10^{-3}$. In the small $r$ limit, $\alpha$-attractors and Dp-brane inflation models describe vertical $\beta$-stripes in the ($n_s$, $r$) space, with $n_s=1-\beta /N$, $\beta =2,\frac{5}{3},\frac{8}{5},\frac{3}{2},\frac{4}{3}$. A phenomenological description of these models and their generalizations can be achieved in the context of pole inflation. Most of the $1\sigma$ area in the ($n_s$, $r$) space favored by Planck 2018 can be covered models with $\beta =2$ and $\beta =5/3$. Future precision data on $n_s$ may help to discriminate between these models even if the precision of the measurement of $r$ is insufficient for the discovery of gravitational waves produced during inflation.

Comments: 20 pages, 11 figures. few typos corrected